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Thermodynamic properties and phase equilibria of Sn–Bi–Zn ternary alloys
Materials Chemistry and Physics 112 (2008) 94–103
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Thermodynamic properties and phase equilibria of Sn–Bi–Zn ternary alloys Ching-feng Yang a , Feng-ling Chen a , Wojciech Gierlotka a,b , Sinn-wen Chen a,∗ , Ker-chang Hsieh c , Li-ling Huang a a
Department of Chemical Engineering, National Tsing Hua University, #101, Section 2, Kuang-Fu Road, Hsin-chu, Taiwan Non-Ferrous Metals Department, AGH University of Science and Technology, Krakow, Poland c Institute of Materials Science and Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan b
a r t i c l e
i n f o
Article history: Received 4 March 2008 Received in revised form 6 May 2008 Accepted 14 May 2008 Keywords: Sn–Bi–Zn Phase equilibria CALPHAD
a b s t r a c t Sn–Bi–Zn alloys are promising Pb-free solders. In this study, their thermodynamic properties and phase equilibrium relationships are determined both experimentally and theoretically. Various Sn–Bi–Zn alloys are prepared, equilibrated at 160 ◦ C, and the equilibrium phases are examined. No ternary compound is found. The isothermal section at 160 ◦ C is proposed based on the ternary phase equilibria data and the phase diagrams of the constituent binary systems. Activities of Sn and Zn of Sn–Zn, Sn–Bi and Sn–Bi–Zn alloys are determined using the electromotive force method. The thermodynamic properties and phase equilibria information determined in this study and those available in the literatures are evaluated. The thermodynamic models of Sn–Bi–Zn phases are assessed, and the isothermal sections, isoplethal section, and liquidus projection of the Sn–Bi–Zn system are calculated using the calculation of phase diagram (CALPHAD) approach. The calculated thermodynamic properties and phase diagrams are consistent with the experimental values. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Pb–Sn solders have been used for over a thousand years. However, due to their toxicity and requirement of the RoHS (restrictions of hazardous substances) regulations, they are now being replaced with the Pb-free solders. Among the various Pb-free solders, the eutectic and near-eutectic Sn–Cu and Sn–Ag–Cu alloys are most highly recommended, and have been studied extensively [1–3]. A major disadvantage of these two alloys is that their melting points are much higher than that of the conventional eutectic Sn–Pb solder. Sn–Bi–Zn and its based alloys are promising solders with lower melting points [4–6]; however, their properties are not very well understood. This study investigates the thermodynamic properties and phase relationships of the Sn–Bi–Zn ternary systems. The activities of Sn and Zn of Sn–Zn, Sn–Bi and Sn–Bi–Zn alloys are experimentally determined using the EMF (electromotive force) method. Phase equilibria of Sn–Bi–Zn ternary alloys are determined using the conventional annealing and metallographic analysis method. The thermodynamic properties and phase equilibria information determined in this study and those obtained from the literature [7–27] are evaluated. Thermodynamic models of Sn–Bi–Zn phases
∗ Corresponding author. Tel.: +886 3 5721734; fax: +886 3 5715408. E-mail address: [email protected] (S.-w. Chen). 0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2008.05.034
are assessed using the calculation of phase diagram (CALPHAD) approach [28,29]. The phase diagrams are then calculated with the assessed models. 2. Experimental procedures Three different kinds of alloys, Sn–Bi, Sn–Zn and Sn–Bi–Zn, were prepared. The alloys were prepared with pure Sn shots, Bi shots, and Zn shots. The suppliers of the pure metals and chemicals used in this study and their purities are summarized in Table 1. Appropriate amounts of pure elements were weighed with an electronic balance (AE200, Mettler, USA), encapsulated in a quartz tube under 10−5 bar vacuum, homogenized at 800 ◦ C for 3 days, removed from the furnace and quenched. For phase equilibria study, the quenched sample capsule was annealed at 160 ◦ C for 10–15 weeks. The equilibrated samples were metallographically analyzed. The microstructures were determined by optical microscopy and SEM (Scanning electron microcopy, JEOL, JSM5600, Japan), the compositions were determined by EPMA (Electron probe microanalysis, JEOL, JXA-8200M), and the structures were determined by XRPD (X-ray powder diffractometer, MAC Science, Japan). For the EMF measurements, a piece of alloy weighing 1.5 g was cut from the quenched ingots and placed inside a small quartz tube of 8 mm o.d. (outside diameter) × 6 mm i.d. (inside diameter) × 25 mm height. The alloy was melted in an argon atmosphere. A 200-mm long W wire of 1.0 mm diameter was immersed in the molten metal and was then cooled to room temperature. The W conduction wire was shielded in a Pyrex tube of 4 mm o.d. × 2.4 mm i.d. × 190 mm height to avoid direct contact with the electrolytes during the EMF measurements. As shown in Fig. 1(a) of the electrodes, the Pyrex tube was sealed with the W wire in the open end, and only 3 mm long W wire was exposed. For the Sn–Bi EMF measurements, pure Sn was used as the reference electrode, and pure Zn was used for those of Sn–Zn and Sn–Bi–Zn alloys. The preparation of the reference electrode was identical to that for the sample electrode as mentioned in the above, except the alloy was replaced with pure Sn and Zn shots.
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Table 2 Compositions of alloys prepared for EMF study
Table 1 Pure metals and chemicals used in this study Metals and chemicals
Purity (wt.%)
Supplier
Sn shots Bi shots Zn shots W wire SnCl2 LiCl KCl CsCl ZnCl2
99.9 99.99 99.99 99.99 99.99 99.6 99.5 99.97 99.8
Showa, Tokyo, Japan Sigma–Aldrich, St. Louis, USA Showa, Tokyo, Japan Sigma–Aldrich, St. Louis, USA Sigma–Aldrich, St. Louis, USA MP Biomedicals, Solon, USA Showa, Tokyo, Japan Noah Technologies, San Antonio, TX ¨ Seelze, Germany Riedel-de Haen,
For the Sn–Bi EMF measurements, the electrolyte was composed of 5 wt.% SnCl2 [30] and 95 wt.% of a eutectic salt mixture consisting of 57.5 at.% LiCl, 13.3 at.% KCl, and 29.2 at.% CsCl. For the Sn–Zn and Sn–Bi–Zn EMF measurements, the electrolyte was the same, except that the SnCl2 was replaced with ZnCl2 . The melting point of the eutectic salt mixture is at 265 ◦ C, and is suitable for EMF measurement at lower temperatures [31]. As shown in Fig. 1(b), proper amounts of the constituents of the electrolyte were contained in a quartz tube of 20 mm o.d. × 18 mm i.d. × 10 mm height, placed in a furnace continuously purged with argon gas, heated up to 500 ◦ C, cooled down and kept at 350 ◦ C for 12 h. The electrolyte was homogeneous and molten at 350 ◦ C. As shown in Fig. 1(c), the sample electrode, reference electrode and a thermocouple shielded with a quartz tube (8 mm o.d. × 6 mm i.d. × 250 mm height) were immersed into the molten electrolyte at 350 ◦ C under the flow of argon gas. The sample electrode was the working electrode, the pure Sn (or Zn) electrode was the reference electrode, and the electric potentials were measured using a potential-
No.
Composition
xSn
xBi
xZn
1 2 3 4 5 6 7 8
Sn–30 at.%Bi Sn–40 at.%Bi Sn–43 at.%Bi Sn–50 at.%Bi Sn–60 at.%Bi Sn–70 at.%Bi Sn–80 at.%Bi Sn–90 at.%Bi
0.70 0.60 0.57 0.50 0.40 0.30 0.20 0.10
0.30 0.40 0.43 0.50 0.60 0.70 0.80 0.90
EMF – – – – – – – –
9 10 11 12 13
Sn–14.9 at.%Zn Sn–20 at.%Zn Sn–30 at.%Zn Sn–40 at.%Zn Sn–50 at.%Zn
0.851 0.80 0.70 0.60 0.50
– – – – –
0.149 0.20 0.30 0.40 0.50
14 15 16 17 18 19 20 21
Sn–1.6 at.%Bi–13.7 at.%Zn Sn–20 at.%Bi–10 at.%Zn Sn–60 at.%Bi–30 at.%Zn Sn–45 at.%Bi–10 at.%Zn Sn–40 at.%Bi–20 at.%Zn Sn–35 at.%Bi–30 at.%Zn Sn–30 at.%Bi–40 at.%Zn Sn–25 at.%Bi–50 at.%Zn
0.847 0.70 0.10 0.45 0.40 0.35 0.30 0.25
0.016 0.20 0.60 0.45 0.40 0.35 0.30 0.25
0.137 0.10 0.30 0.10 0.20 0.30 0.40 0.50
stat (Model 602A electrochemical analyzer, CH instruments, Austin, USA). The three different kinds of cells used in this study are listed in the following: Cell I for Sn–Bi : (−)W/Sn(1) /SnCl2 + KCl + LiCl + CsCl2(1) /Sn–Bi(1) /W(+) Cell II for Sn–Zn : (−)W/Zn(1) /ZnCl2 + KCl + LiCl + CsCl2(1) /Sn–Zn(1) /W(+) Cell III for Sn–Bi–Zn : (−)W/Zn(1) /ZnCl2 + KCl + LiCl + CsCl2(1) /Sn–Bi–Zn(1) /W(+)
3. Results and discussion 3.1. EMF measurements Eight Sn–Bi alloys were prepared and their compositions are listed in Table 2. Fig. 2(a) shows the measured potential versus reaction time of the Sn/Sn2+ /Sn–90 at.%Bi system and Fig. 2(b) shows the relationship of the furnace temperature with the reaction time. The average potential of the Sn/Sn2+ /Sn–90 at.%Bi system at a certain temperature can then be determined from the data shown in Fig. 2(a) and (b). For example, the average potential is 52.4 mV at 304 ◦ C and is 70.3 mV at 498 ◦ C. Fig. 2(c) is the plot between the determined average potential versus temperature. A linear relationship of the potential and the reaction temperature is found. As shown in Table 3, the relationship is determined to be E = −1.163 + 0.0928T where E is mV and T is in Kelvin. Similar linear relationships of the EMF results of other Sn–Bi alloys are found and are shown in Fig. 3 and Table 3.
Table 3 Sn potential as a function of temperature in the Sn/Sn2+ /Sn–Bi system
Fig. 1. Schematic diagram of the EMF apparatus: (a) connection of lead wires and electrodes, (b) electrolyte preparation and (c) cell construction.
No.
xSn
A (mV)
1 2 3 4 5 6 7 8
0.70 0.60 0.57 0.50 0.40 0.30 0.20 0.10
0.281 −3.723 −2.233 −0.841 −0.783 −1.090 −1.981 −1.163
B (mV/K) ± ± ± ± ± ± ± ±
0.209 0.353 0.692 0.608 0.302 0.886 0.745 0.448
0.0141 0.0242 0.0264 0.0280 0.0369 0.0493 0.0660 0.0928
± ± ± ± ± ± ± ±
0.0003 0.0005 0.0010 0.0009 0.0004 0.0013 0.0011 0.0007
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Fig. 3. The relationship between potential and temperature of Sn–Bi alloys.
dynamic relationships with the determined potentials. GSn = −nFε = RT ln aSn
H Sn = nF T
S Sn = nF
∂ε ∂T
∂ε ∂T
−ε
where ε is the electromotive force of the cell, F is the Faraday constant (96,486 C mole−1 ), R is the universal gas constant (8.311434 J mole−1 K−1 )), T is the absolute temperature, and n is the number of electrons in reaction. Figs. 8(a)–(c) show the activities of Sn in the Sn–Bi alloys, Sn–Zn alloys, and the activities of Zn in the Sn–Bi–Zn alloys, respectively. The experimental results of this study are in agreement with the data available in the literature [7–9,11,12,26]. All activities in each system show a positive deviation from the ideal solution. Other thermodynamic properties, such as partial Gibbs free energies, partial enthalpies, and Table 4 Zn potential as a function of temperature in the Zn/Zn2+ /Sn–Zn system
Fig. 2. In the Sn/Sn2+ /Sn–90 at.%Bi system: (a) potential vs. time, (b) temperature vs. time and (c) potential vs. temperature.
Five different Sn–Zn alloys are prepared and their compositions are listed in Table 2. Fig. 4(a) and (b) shows the determined potential and furnace temperature versus reaction time of the Zn/Zn2+ /Sn–20 at.%Zn, respectively. With similar procedures, the relationship between the potential and the reaction temperature can be determined as shown in Fig. 4(c). Similar linear relationships are observed for the Sn–Zn alloys of different compositions and the results are summarized in Table 4 and Fig. 5. Eight Sn–Bi–Zn alloys were prepared. Similar linear relationship between the Zn potential and temperature from the EMF results are found, and the results are shown in Figs. 6 and 7 and Table 5. The partial free energies, activities, and partial enthalpies can then be determined from the measured potential versus reaction temperature relationship. The following equations are the thermo-
No.
xZn
A (mV)
9 10 11 12 13
0.149 0.20 0.30 0.40 0.50
−43.852 −42.043 −34.491 −28.286 −18.788
B (mV/K) ± ± ± ± ±
1.326 0.546 0.404 0.545 1.173
0.1139 0.0994 0.0755 0.0594 0.0381
± ± ± ± ±
0.0017 0.0007 0.0005 0.0007 0.0015
Table 5 Zn potential as a function of temperature in the Zn/Zn2+ /Sn–Bi–Zn system No.
xSn
xBi
xZn
A (mV)
B (mV/K)
14 15 16
0.847 0.70 0.10
0.016 0.20 0.60
0.137 0.10 0.30
−45.062 ± 0.958 −49.981 ± 1.620 −43.910 ± 0.673
0.1174 ± 0.0012 0.1322 ± 0.0021 0.0736 ± 0.0009
No.
xZn
A (mV)
xSn /xBi = 1/1 17 18 19 20 21
0.10 0.20 0.30 0.40 0.50
−50.367 −44.545 −37.519 −30.731 −22.885
B (mV/K) ± ± ± ± ±
0.751 0.563 0.813 0.190 0.475
0.1270 0.0942 0.0718 0.0546 0.0376
± ± ± ± ±
0.0010 0.0007 0.0010 0.0002 0.0006
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small amount of Sn and Zn solubility. The composition of dark phase is Sn–0.2 at.%Bi–99.7 at.%Zn, and is the Zn phase with almost no Sn and Bi. The remaining is a fine-structure region composed of various phases, and its average composition is Sn–32.0 at.%Bi–10.5 at.%Zn. This fine-structure phase region is likely the liquid phase at 160 ◦ C prior to its removal from the furnace. Three different phases can be found in the fine-structure phase region, and they are the Bi, Zn and Sn phases based on the elemental X-ray mapping. Since the liquid phase region is in fact composed of different phases, the compositions vary locally, and thus the uncertainty in the liquid composition measurement is high. Fig. 9(b) is the XRD pattern of alloy no. 26, in which the characteristic peaks of Sn, Bi, and Zn phases are found. The XRD results agree with the microstructural analysis data. The equilibrium phases of alloy no. 26 are Bi, Zn and liquid phases at 160 ◦ C, and the liquid phase transforms into Sn, Bi and Zn phases when it is quenched to the room temperature. Similar results are found for alloy no. 28, and all these alloys are in the Bi–Zn-liquid three-phase tie-triangle region. Fig. 10(a) is the BEI micrograph of alloy no. 29 (Sn–15 at.%Bi–30 at.%Zn) annealed at 160 ◦ C, and it has three different phase regions. The composition of the largest and grey phase is Sn–7.6 at.%Bi–1.9 at.%Zn and is the Sn phase. The composition of the darkest phase is Sn–97.0 at.%Zn and is the Zn phase. The remaining phase region is composed of various phases and its average composition is Sn–25.0 at.%Bi–10.9 at.%Zn. Similar to the fine-structure phase region in the alloy no. 26, this phase region was the liquid phase prior to quenching. The XRD pattern of alloy no. 29 is shown in Fig. 10(b), and the diffraction peaks of Sn, Zn, and Bi phases are observed. The alloy no. 29 is in the Sn–Zn–liquid tie-triangle at 160 ◦ C. Similar results are found for alloy no. 27, and it is also in the Sn–Zn–liquid tie-triangle at 160 ◦ C. Fig. 11 is the BEI micrograph of alloy no. 22 (Sn–60 at.%Bi–2.5 at.%Zn) annealed at 160 ◦ C, and there are two phase regions. As listed in Table 7, the composition of the bright phase determined by EDS is Sn–96.3 at.%Bi–0.21 at.%Zn (Bi phase). The other phase region is composed of three phases. Similar to those mentioned above, it was the liquid phase at 160 ◦ C. The alloy no. 22 is in the Bi-liquid two-phase region at 160 ◦ C. Fig. 12 shows the BEI micrograph of alloy no. 23 (Sn–22.5 at.%Bi–2.5 at.%Zn) equilibrated at 160 ◦ C. The composition of the darker phase is Sn–5.0 at.%Bi–0.5 at.%Zn and is the Sn phase. The brighter phase region has various phases and its average composition is Sn–27.0 at.%Bi–3.0 at.%Zn and was the liquid phase at 160 ◦ C. Alloy no. 23 is in the Sn–liquid two-phase region. Fig. 13
Fig. 4. In the Zn/Zn2+ /Sn–20 at.%Zn system: (a) potential vs. time, (b) temperature vs. time and (c) potential vs. temperature.
partial entropies, are also determined in this study as can be seen in Table 6. 3.2. Phase equilibria Eight alloys were prepared and annealed at 160 ◦ C, and their compositions are shown in Table 7. As shown in Fig. 9(a), three-phase regions can be observed in the BEI (backscattered electron image) micrograph of alloy no. 26 (Sn–70 at.%Bi–10 at.%Zn) annealed at 160 ◦ C. The larger and brighter phase has a composition of Sn–98.6 at.%Bi–0.8 at.%Zn, and probably is the Bi phase with
Fig. 5. The relationship between potential and temperature of Sn–Zn alloys.
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Table 6 Partial molar properties of Sn–Bi, Sn–Zn and Sn–Bi–Zn alloys No.
xSn
GSn (J mole−1 )
aSn
H Sn (J mole−1 )
S Sn (J mole−1 K−1 )
◦
Partial molar properties of Sn in Sn–Bi alloys at 300 C (573 K) 1 0.10 0.1216 −10037 224 17.9 2 0.20 0.2342 −6915 382 12.7 3 0.30 0.3328 −5241 210 9.5 4 0.40 0.4384 −3929 151 7.1 5 0.50 0.5402 −2934 162 5.4 6 0.57 0.5932 −2488 431 5.1 7 0.60 0.6631 −1957 718 4.7 8 0.70 0.7292 −1613 −54 2.7 No.
GZn (J mole−1 )
aZn
xZn
H Zn (J mole−1 )
S Zn (J mole−1 K−1 )
◦
Partial molar properties of Zn in Sn–Zn alloys at 440 C (713 K) 9 0.149 0.2964 −7209 8462 10 0.20 0.3912 −5563 8113 11 0.30 0.5328 −3732 6656 12 0.40 0.6326 −2714 5458 13 0.50 0.7613 −1617 3626 No.
GZn (J mole−1 )
aZn
xZn
H Zn (J mole−1 )
22.0 19.2 14.6 11.5 7.4 S Zn (J mole−1 K−1 )
◦
Partial molar properties of Zn in Sn–Bi–Zn alloys at 440 C (713 K) 14 0.137 0.2842 −7457 8696 22.7 15 0.10 0.2366 −8544 9645 25.5 16 0.30 0.7566 −1653 8473 14.2 No. xZn
GZn (J mole−1 ) H Zn (J mole−1 ) S Zn (J mole−1 K−1 )
aZn
Partial molar properties of Zn in Sn–Bi–Zn alloys at 440 ◦ C (713 K) xSn /xBi = 1/1 17 0.10 0.2703−7754 9719 24.5 18 0.20 0.4789−4365 8596 18.2 19 0.30 0.6407−2639 7240 13.9 20 0.40 0.7657−1582 5930 10.5 21 0.50 0.8801 −757 4416 7.3
Table 7 Phase equilibria of Sn–Bi–Zn alloys at 160 ◦ C No.
Nominal composition xSn
xBi
Equilibrium Phases
xZn
Compositions xSn
xZn
xBi
0.025
L Bi
0.623 0.016
0.013 0.021
0.364 0.963
0.75
0.225 0.025
L Sn
0.7 0.945
0.03 0.005
0.27 0.05
24
0.45
0.45
0.10
L Zn
0.499 0.007
0.084 0.992
0.417 0.001
25
0.6
0.30
0.10
L Zn
0.683 0.005
0.039 0.995
0.278 0
26
0.2
0.7
0.10
L Bi Zn
0.575 0.006 0.001
0.105 0.008 0.997
0.32 0.986 0.002
27
0.75
0.15
0.10
L Sn Zn
0.652 0.892 0.015
0.097 0.024 0.981
0.251 0.084 0.004
28
0.30
0.40
0.30
L Bi Zn
0.579 0 0.005
0.097 0.016 0.99
0.324 0.984 0.005
29
0.55
0.15
0.30
L Sn Zn
0.641 0.905 0.03
0.109 0.019 0.97
0.25 0.076 0
22
0.375 0.60
23
Note. The uncertainty of the liquid composition is high. Segregation occurs and various solid phases form in the liquid phase region when the sample is removed from the furnace, and thus regional variation of composition in the originally liquid phase region is high.
Fig. 6. In the Zn/Zn2+ /Sn–20 at.%Bi–10 at.%Zn system: (a) potential vs. time, (b) temperature vs. time and (c) potential vs. temperature.
is the 160 ◦ C isothermal section of the Sn–Bi–Zn ternary system based on the experimental analyses of the ten equilibrated alloys. No ternary compound is found, and there are two three-phase regions, Bi–Zn–Liquid and Sn–Zn–Liquid, in the ternary system at 160 ◦ C. 3.3. Thermodynamic modeling Thermodynamic models of the three constituent binary systems, Sn–Zn, Sn–Bi and Bi–Zn are needed for the calculation of the Sn–Bi–Zn phase equilibria using the CALPHAD approach. The
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parameters of the Bi–Zn system assessed by Malakhov [10] are used directly. Thermodynamic parameters for the phases in the Sn–Zn, Sn–Bi and Sn–Bi–Zn systems were optimized using ThermoCalc [32] and Pandat software [33]. There are liquid, Sn (BCT A5), Bi (Rhombohedral A7) and practically pure Zn (HCP ZN) phases, and no binary and ternary compounds. The Gibbs free energies of the pure elements Sn, Bi and Zn are taken from the SGTE database [34]. Since the solubility in Zn phase is very small, it is treated as pure element in this study. Gibbs free energies of mixing for each solution phase, i.e. liquid, Sn (BCT A5) and Bi (Rhombohedral A7), are described by the following equation: Gm (T ) =
xi Gi0 (T ) + RT
i
xi ln xi
i
Fig. 7. The relationship between potential and temperature of Sn–Bi–Zn alloys.
+
i
j>i
xi xj
v
Lij (xi − xj )
v
v
Fig. 8. (a) Activities of Sn in Sn–Bi alloys, (b) activities of Zn in Sn–Zn alloys and (c) activities of Zn in Sn–Bi–Zn alloys.
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Fig. 11. BEI micrograph of alloy no. 22 (Sn–60 at.%Bi–2.5 at.%Zn) annealed at 160 ◦ C for 10 weeks.
Fig. 9. (a) BEI micrograph of alloy no. 26 (Sn–70 at.%Bi–10 at.%Zn) annealed at 160 ◦ C for 15 weeks and (b) XRD pattern of alloy no. 26 annealed at 160 ◦ C for 15 weeks.
Fig. 12. BEI micrograph of alloy no. 23 (Sn–22.5 at.%Bi–2.5 at.%Zn) annealed at 160 ◦ C for 10 weeks.
Fig. 10. (a) BEI micrograph of alloy no. 29 (Sn–15 at.%Bi–30 at.%Zn) annealed at 160 ◦ C for 15 weeks and (b) XRD pattern of alloy no. 29 annealed at 160 ◦ C for 15 weeks.
Fig. 13. Isothermal section of the Sn–Bi–Zn ternary system at 160 ◦ C.
C.-f. Yang et al. / Materials Chemistry and Physics 112 (2008) 94–103 Table 8 Thermodynamic parameters of the Sn–Bi–Zn system System
Parameters
Sn–Bi
0 liq LBiSn = 575.3621+1.2470T 1 liq LBiSn = −27.1141 − 0.2695T 0 BCT A5 LBiSn = 2340.9429 − 1.0836T 1 BCT A5 LBiSn = −3.096.9418 0 Rhombohedral A7 LBiSn = 20574.8595 − 22.6000T 0 Rhombohedral A7 LBiSn = −5769.0000 + 14.7401T
Sn–Zn
0 liq LSnZn = 21468.89 − 100.79T + 12.00T ln T 1 liq LSnZn = −6355.40 + 12.38T − 1.12T ln T ) 2 liq LSnZn = 2624.86 − 1.52T 0 HCP Zn LSnZn = 4941.62 + 5.00T 0 BCT A5 LSnZn = 6772.15 + 24.15T
Bi–Zn
0 liq LBiZn = 18265.09 − 8.6763T 1 liq LBiZn = −6061.21 + 0.79581T 2 liq LBiZn = −6422.6 + 11.71966T 3 liq LBiZn = 7227.44 − 9.2905T 4 liq LBiZn = 21123.07 − 27.14705T 5 liq LBiZn = −20747.56 + 22.01759T 6 liq LBiZn = −7600.36 + 13.15957T 0 HCP Zn LBiZn = 25,000 0 Rhombohedral A7 LBiZn = 10, 000
Sn–Bi–Zn
0 liq LBiSnZn 1 liq LBiSnZn 3 liq LBiSnZn
= −39083.23 + 34.81T = −5617.41 + 6.73T = 2.737.35 − 2.48T
where Gi0 is the molar Gibbs free energy of pure tin, bismuth, or zinc, xi is the molar fraction of the component “i”, R is the gas constant, and T is the absolute temperature. Interaction parameter of the solution v Lij is given by the following equation: v
Lij = Av + Bv T + Cv T ln T
Thermochemical and phase equilibria data obtained from the literature [7–27] and this study are used for optimization.
101
Table 9 Experimental and calculated ternary eutectic point
Experiment [24] This work Malakhov [23] Moelans [22]
T [◦ C]
xBi
xSn
135 ± 0.5 135.9 130 132
0.41 0.39 0.39 0.36
0.57 0.56 0.54 0.58
The thermodynamic parameters determined are summarized in Table 8. The calculated activities of Zn in the Sn–Zn system are superimposed with the experimental data as shown in Fig. 8(b), and are in good agreement with the experimental data [9,11,12]. Fig. 14(a) shows the molar enthalpy of mixing of the Sn–Zn liquid phase. Previous optimization of the Sn–Zn system was done by Ohtani et al. [13] where the enthalpy of mixing was described without temperature dependency. A temperature-dependent model is used to describe the enthalpy of mixing in this study. As shown in Fig. 14(a), the calculated enthalpies of mixing at 433 and 525 ◦ C are in good agreement with the experimental results [14–16], and the agreement is better than that of the previous modeling results [13]. Fig. 14(b) shows the Sn–Zn phase diagram. The eutectic temperature is at 199.1 ◦ C. As can be seen in Fig. 14(b), the calculated liquidus and phase boundaries are in agreement with the experimental boundary data [9,12,17,18]. Similar to those in the Sn–Zn binary system, the activities of Sn in Sn–Bi system, partial enthalpies of mixing of liquid phase of the Sn–Bi system, and the Sn–Bi phase diagram are shown in Figs. 8(a) and 15(a) and (b), respectively. The eutectic temperature is at 139.9 ◦ C, and the calculated thermodynamic properties and phase equilibria are in good agreement with the experimental results [7,8,19–22]. The activities of zinc and the enthalpies of mixing of the liquid phase in the ternary Sn–Bi–Zn system are shown in Figs. 8(c) and 16(a) and (b). The calculated results obtained in this study and the previous optimizations [23,24] all are in good agreement with the experimental data [25,26]. Fig. 16(c) is the isopleth in Sn–Bi–Zn system at a constant fraction of Zinc equal to 0.05 mole fraction. Compared with the previous modeling results [23,24], the calculated boundary of this study very well fit to the experimental
Fig. 14. (a) Enthalpy of mixing in the binary Sn–Zn system and (b) phase diagram of the Sn–Zn system.
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Fig. 15. (a) Partial enthalpy of mixing in the binary Sn–Bi system and (b) phase diagram of Sn–Bi system.
Fig. 16. (a) Activity of Zn in the ternary Sn–Bi–Zn system at xZn = 0.2, (b) enthalpy of mixing in the ternary Sn–Bi–Zn system at xSn /xZn = 3/7 and (c) isoplethal section of the ternary Sn–Bi–Zn system at xZn = 0.05.
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equilibria data determined in this study and those in the literatures, the thermodynamic models of the Sn–Bi–Zn ternary system have been successfully assessed. In the ternary Sn–Bi–Zn system, there are two tie-triangles, liquid + Bi + Zn and liquid + Sn + Zn, at 160 ◦ C, and there is one invariant reaction, liquid = Sn + Bi + Sn, at 135.9 ◦ C and Sn–39 at.%Bi–5 at.%Zn Acknowledgements The authors acknowledge the financial support from the National Science Council of Taiwan (NSC 95-2218-E-007-028). Authors also are grateful to the National Center for Highperformance Computing for the use of PANDAT software. References
Fig. 17. Liquidus projection of Sn–Bi–Zn system.
solidus line [25], while the earlier studies reported a slightly lower temperature [25,26]. The calculated 160 ◦ C isothermal section is shown in Fig. 13. The phase relationships determined from the calculation are in agreement with experimental data. The calculated composition of Bi phase at 160 ◦ C equals xBi = 0.974, xSn = 0.017, xZn = 0.008, and is consistent with the experimental data of this study. Braga et al. [27] determined the Sn–Bi–Zn isothermal section at 100 ◦ C, and they report a much higher Zn solubility of 3.7 wt.% Zn. According to the Bi–Zn binary system [10], the Zn solubility in Bi is 0.4 at.% at 100 ◦ C and 0.9 at.% at 160 ◦ C. Braga et al. [27] had also found the solubility of Zn in Bi phase to be 0.3 wt.% ± 0.1 at 200 ◦ C. Although the addition of Sn might alter the solubility of Zn in Bi, it is still very unlikely if it could make such dramatic difference. Considering those inconsistencies, the data of Braga et al. [27] were not taken into consideration in the modeling processes. The calculated liquids projection is shown in Fig. 17. The ternary eutectic point was experimentally determined by Luef [25] at 135 ◦ C and Sn–41 at.%Bi–2 at.%Zn. The calculated result of this study confirms that it is a type I reaction, liquid = Sn + Bi + Zn, at 135.9 ◦ C and Sn–39 at.%Bi–5 at.%Zn. As summarized in Table 9, the calculated results determined in this study are in better agreement than those modeling results reported previously [23,24]. 4. Conclusions There are no binary and ternary compounds found in the Sn–Bi–Zn system at 160 ◦ C. Based on the thermodynamic and phase
[1] A. Rae, A. Handwerker, NEMI’s Lead-Free Alloy, Circuits Assembly, 2004, pp. 20–25. [2] K.J. Puttlitz, K.A. Stalter, Handbook of Lead-Free Solder Technology for Microelectronic Assemblies, Marcel Dekker, New York, 2004, pp. 239–300. [3] C.-H. Wang, S.-W. Chen, Acta Mater. 54 (1) (2006) 247–253. [4] M. McCormack, S. Jin, J. Electron. Mater. 23 (1994) 715–720. [5] S.W. Yoon, J.R. Soh, H.M. Lee, B.J. Lee, Acta Mater. 45 (1997) 951–960. [6] Y.S. Kim, K.S. Kim, C.W. Hwang, K. Suganuma, J. Alloys Compd. 352 (2003) 237–245. [7] N.A. Asryan, A. Mikula, Inorg. Mater. 40 (4) (2004) 386–390. [8] H. Seltz, F.J. Dunkerlej, J. Am. Chem. Soc. 64 (1942) 1392. [9] Z. Moser, W. Gasior, Bull. Polish Acad. Sci. Tech. Sci. 31 (1983) 19–25. [10] D.V. Malakhov, Calphad, 24 no. 1, 1. [11] V.N.S. Mathur, M.L. Kapoor, Indian J. Pure Appl. Phys. 23 (1985) 370. [12] W. Ptak, Thermodynamic properties of liquid zinc–tin solutions, Archiwum Hutnictwa 2 (1960) 169–194. [13] H. Ohtani, M. Miyashita, K. Ishida, J. Jpn. Inst. Met. 63 (1999) 685. [14] O.J. Kleppa, J. Phys. Chem 59 (1955) 354. [15] M. Fiorani, V. Valenti, Gazz. Chim. Ital. 85 (1955) 607. [16] N.W. Taylor, J. Am. Chem. Soc. 45 (1923) 2865. [17] B. Strauss, B. Dobovisek, Rudarsko Met. Sbornik 3 (1960) 273. [18] F. Vnuk, M.H. Ainsley, The solid solubility of silver, gold, and zinc in metallic tin, J. Mater. Sci. 16 (1981) 1171–1176. [19] M. Kawakami, Z. Anorg. Allg. Chem. 167 (1927) 345. [20] W. Oelsen, P. Zuhlke, Arch. Eisenhuttenwes 27 (1956) 743. [21] S. Nagasaki, E. Fujita, J. Jpn. Inst. Met. 16 (1952) 313. [22] K. Ishida, H. Ohtani, J. Electron. Mater. 23 (1994) 603. [23] N. Moelans, K.C. Hari Kumar, P. Wollants, J. Alloys Compd. 360 (2003) 98. [24] D.V. Malakhov, X.J. Liu, I. Okhuma, K. Ishida, J. Phase Equilib. 21 (6) (2000) 514–520. [25] C. Luef, P. Aloke, J. Vizdal, A. Kroupa, A. Kodentsov, H. Ipser, Monatsh. Chem. 137 (2006) 381. [26] W. Ptak, Z. Moser, Archiwum Hutnictwa 11 (1966) 289–324. [27] M.H. Braga, J. Vizdal, A. Krupa, J. Ferreira, D. Soares, L.F. Malheiros, Calphad 31 (4) (2007) 468–478. [28] N. Saunders, P. Miodownik, Calphad, Calculation of Phase Diagrams a Comprehensive Guide, Elsevier Science, Oxford, UK, 1998. [29] H. Okamoto, T.B. Massalski, Guidelines for binary phase diagrams assessment, J. Phase Equilib. 14 (1993) 316. [30] K. Kameda, T. Azakami, Trans. Jpn. Inst. Metals 41 (1976) 1087–1092. [31] H. Ito, Y. Hasegawa, J. Chem. Eng. Data 46 (2001) 1203–1205. [32] V.Q. ThermoCalc, Fundation Computational Thermodynamic, Stockholm, Sweden, 2000. [33] Pandat, CompuTherm LLC, 437 S. Yellowstone Dr. Suite 217 Madison, WI 53719, USA. [34] A. Dinsdale, SGTE data for pure elements, Calphad 15 (1991) 317–425.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Thermodynamic properties and phase equilibria of Sn–Bi–Zn ternary alloys Ching-feng Yang a , Feng-ling Chen a , Wojciech Gierlotka a,b , Sinn-wen Chen a,∗ , Ker-chang Hsieh c , Li-ling Huang a a
Department of Chemical Engineering, National Tsing Hua University, #101, Section 2, Kuang-Fu Road, Hsin-chu, Taiwan Non-Ferrous Metals Department, AGH University of Science and Technology, Krakow, Poland c Institute of Materials Science and Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan b
a r t i c l e
i n f o
Article history: Received 4 March 2008 Received in revised form 6 May 2008 Accepted 14 May 2008 Keywords: Sn–Bi–Zn Phase equilibria CALPHAD
a b s t r a c t Sn–Bi–Zn alloys are promising Pb-free solders. In this study, their thermodynamic properties and phase equilibrium relationships are determined both experimentally and theoretically. Various Sn–Bi–Zn alloys are prepared, equilibrated at 160 ◦ C, and the equilibrium phases are examined. No ternary compound is found. The isothermal section at 160 ◦ C is proposed based on the ternary phase equilibria data and the phase diagrams of the constituent binary systems. Activities of Sn and Zn of Sn–Zn, Sn–Bi and Sn–Bi–Zn alloys are determined using the electromotive force method. The thermodynamic properties and phase equilibria information determined in this study and those available in the literatures are evaluated. The thermodynamic models of Sn–Bi–Zn phases are assessed, and the isothermal sections, isoplethal section, and liquidus projection of the Sn–Bi–Zn system are calculated using the calculation of phase diagram (CALPHAD) approach. The calculated thermodynamic properties and phase diagrams are consistent with the experimental values. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Pb–Sn solders have been used for over a thousand years. However, due to their toxicity and requirement of the RoHS (restrictions of hazardous substances) regulations, they are now being replaced with the Pb-free solders. Among the various Pb-free solders, the eutectic and near-eutectic Sn–Cu and Sn–Ag–Cu alloys are most highly recommended, and have been studied extensively [1–3]. A major disadvantage of these two alloys is that their melting points are much higher than that of the conventional eutectic Sn–Pb solder. Sn–Bi–Zn and its based alloys are promising solders with lower melting points [4–6]; however, their properties are not very well understood. This study investigates the thermodynamic properties and phase relationships of the Sn–Bi–Zn ternary systems. The activities of Sn and Zn of Sn–Zn, Sn–Bi and Sn–Bi–Zn alloys are experimentally determined using the EMF (electromotive force) method. Phase equilibria of Sn–Bi–Zn ternary alloys are determined using the conventional annealing and metallographic analysis method. The thermodynamic properties and phase equilibria information determined in this study and those obtained from the literature [7–27] are evaluated. Thermodynamic models of Sn–Bi–Zn phases
∗ Corresponding author. Tel.: +886 3 5721734; fax: +886 3 5715408. E-mail address: [email protected] (S.-w. Chen). 0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2008.05.034
are assessed using the calculation of phase diagram (CALPHAD) approach [28,29]. The phase diagrams are then calculated with the assessed models. 2. Experimental procedures Three different kinds of alloys, Sn–Bi, Sn–Zn and Sn–Bi–Zn, were prepared. The alloys were prepared with pure Sn shots, Bi shots, and Zn shots. The suppliers of the pure metals and chemicals used in this study and their purities are summarized in Table 1. Appropriate amounts of pure elements were weighed with an electronic balance (AE200, Mettler, USA), encapsulated in a quartz tube under 10−5 bar vacuum, homogenized at 800 ◦ C for 3 days, removed from the furnace and quenched. For phase equilibria study, the quenched sample capsule was annealed at 160 ◦ C for 10–15 weeks. The equilibrated samples were metallographically analyzed. The microstructures were determined by optical microscopy and SEM (Scanning electron microcopy, JEOL, JSM5600, Japan), the compositions were determined by EPMA (Electron probe microanalysis, JEOL, JXA-8200M), and the structures were determined by XRPD (X-ray powder diffractometer, MAC Science, Japan). For the EMF measurements, a piece of alloy weighing 1.5 g was cut from the quenched ingots and placed inside a small quartz tube of 8 mm o.d. (outside diameter) × 6 mm i.d. (inside diameter) × 25 mm height. The alloy was melted in an argon atmosphere. A 200-mm long W wire of 1.0 mm diameter was immersed in the molten metal and was then cooled to room temperature. The W conduction wire was shielded in a Pyrex tube of 4 mm o.d. × 2.4 mm i.d. × 190 mm height to avoid direct contact with the electrolytes during the EMF measurements. As shown in Fig. 1(a) of the electrodes, the Pyrex tube was sealed with the W wire in the open end, and only 3 mm long W wire was exposed. For the Sn–Bi EMF measurements, pure Sn was used as the reference electrode, and pure Zn was used for those of Sn–Zn and Sn–Bi–Zn alloys. The preparation of the reference electrode was identical to that for the sample electrode as mentioned in the above, except the alloy was replaced with pure Sn and Zn shots.
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Table 2 Compositions of alloys prepared for EMF study
Table 1 Pure metals and chemicals used in this study Metals and chemicals
Purity (wt.%)
Supplier
Sn shots Bi shots Zn shots W wire SnCl2 LiCl KCl CsCl ZnCl2
99.9 99.99 99.99 99.99 99.99 99.6 99.5 99.97 99.8
Showa, Tokyo, Japan Sigma–Aldrich, St. Louis, USA Showa, Tokyo, Japan Sigma–Aldrich, St. Louis, USA Sigma–Aldrich, St. Louis, USA MP Biomedicals, Solon, USA Showa, Tokyo, Japan Noah Technologies, San Antonio, TX ¨ Seelze, Germany Riedel-de Haen,
For the Sn–Bi EMF measurements, the electrolyte was composed of 5 wt.% SnCl2 [30] and 95 wt.% of a eutectic salt mixture consisting of 57.5 at.% LiCl, 13.3 at.% KCl, and 29.2 at.% CsCl. For the Sn–Zn and Sn–Bi–Zn EMF measurements, the electrolyte was the same, except that the SnCl2 was replaced with ZnCl2 . The melting point of the eutectic salt mixture is at 265 ◦ C, and is suitable for EMF measurement at lower temperatures [31]. As shown in Fig. 1(b), proper amounts of the constituents of the electrolyte were contained in a quartz tube of 20 mm o.d. × 18 mm i.d. × 10 mm height, placed in a furnace continuously purged with argon gas, heated up to 500 ◦ C, cooled down and kept at 350 ◦ C for 12 h. The electrolyte was homogeneous and molten at 350 ◦ C. As shown in Fig. 1(c), the sample electrode, reference electrode and a thermocouple shielded with a quartz tube (8 mm o.d. × 6 mm i.d. × 250 mm height) were immersed into the molten electrolyte at 350 ◦ C under the flow of argon gas. The sample electrode was the working electrode, the pure Sn (or Zn) electrode was the reference electrode, and the electric potentials were measured using a potential-
No.
Composition
xSn
xBi
xZn
1 2 3 4 5 6 7 8
Sn–30 at.%Bi Sn–40 at.%Bi Sn–43 at.%Bi Sn–50 at.%Bi Sn–60 at.%Bi Sn–70 at.%Bi Sn–80 at.%Bi Sn–90 at.%Bi
0.70 0.60 0.57 0.50 0.40 0.30 0.20 0.10
0.30 0.40 0.43 0.50 0.60 0.70 0.80 0.90
EMF – – – – – – – –
9 10 11 12 13
Sn–14.9 at.%Zn Sn–20 at.%Zn Sn–30 at.%Zn Sn–40 at.%Zn Sn–50 at.%Zn
0.851 0.80 0.70 0.60 0.50
– – – – –
0.149 0.20 0.30 0.40 0.50
14 15 16 17 18 19 20 21
Sn–1.6 at.%Bi–13.7 at.%Zn Sn–20 at.%Bi–10 at.%Zn Sn–60 at.%Bi–30 at.%Zn Sn–45 at.%Bi–10 at.%Zn Sn–40 at.%Bi–20 at.%Zn Sn–35 at.%Bi–30 at.%Zn Sn–30 at.%Bi–40 at.%Zn Sn–25 at.%Bi–50 at.%Zn
0.847 0.70 0.10 0.45 0.40 0.35 0.30 0.25
0.016 0.20 0.60 0.45 0.40 0.35 0.30 0.25
0.137 0.10 0.30 0.10 0.20 0.30 0.40 0.50
stat (Model 602A electrochemical analyzer, CH instruments, Austin, USA). The three different kinds of cells used in this study are listed in the following: Cell I for Sn–Bi : (−)W/Sn(1) /SnCl2 + KCl + LiCl + CsCl2(1) /Sn–Bi(1) /W(+) Cell II for Sn–Zn : (−)W/Zn(1) /ZnCl2 + KCl + LiCl + CsCl2(1) /Sn–Zn(1) /W(+) Cell III for Sn–Bi–Zn : (−)W/Zn(1) /ZnCl2 + KCl + LiCl + CsCl2(1) /Sn–Bi–Zn(1) /W(+)
3. Results and discussion 3.1. EMF measurements Eight Sn–Bi alloys were prepared and their compositions are listed in Table 2. Fig. 2(a) shows the measured potential versus reaction time of the Sn/Sn2+ /Sn–90 at.%Bi system and Fig. 2(b) shows the relationship of the furnace temperature with the reaction time. The average potential of the Sn/Sn2+ /Sn–90 at.%Bi system at a certain temperature can then be determined from the data shown in Fig. 2(a) and (b). For example, the average potential is 52.4 mV at 304 ◦ C and is 70.3 mV at 498 ◦ C. Fig. 2(c) is the plot between the determined average potential versus temperature. A linear relationship of the potential and the reaction temperature is found. As shown in Table 3, the relationship is determined to be E = −1.163 + 0.0928T where E is mV and T is in Kelvin. Similar linear relationships of the EMF results of other Sn–Bi alloys are found and are shown in Fig. 3 and Table 3.
Table 3 Sn potential as a function of temperature in the Sn/Sn2+ /Sn–Bi system
Fig. 1. Schematic diagram of the EMF apparatus: (a) connection of lead wires and electrodes, (b) electrolyte preparation and (c) cell construction.
No.
xSn
A (mV)
1 2 3 4 5 6 7 8
0.70 0.60 0.57 0.50 0.40 0.30 0.20 0.10
0.281 −3.723 −2.233 −0.841 −0.783 −1.090 −1.981 −1.163
B (mV/K) ± ± ± ± ± ± ± ±
0.209 0.353 0.692 0.608 0.302 0.886 0.745 0.448
0.0141 0.0242 0.0264 0.0280 0.0369 0.0493 0.0660 0.0928
± ± ± ± ± ± ± ±
0.0003 0.0005 0.0010 0.0009 0.0004 0.0013 0.0011 0.0007
96
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Fig. 3. The relationship between potential and temperature of Sn–Bi alloys.
dynamic relationships with the determined potentials. GSn = −nFε = RT ln aSn
H Sn = nF T
S Sn = nF
∂ε ∂T
∂ε ∂T
−ε
where ε is the electromotive force of the cell, F is the Faraday constant (96,486 C mole−1 ), R is the universal gas constant (8.311434 J mole−1 K−1 )), T is the absolute temperature, and n is the number of electrons in reaction. Figs. 8(a)–(c) show the activities of Sn in the Sn–Bi alloys, Sn–Zn alloys, and the activities of Zn in the Sn–Bi–Zn alloys, respectively. The experimental results of this study are in agreement with the data available in the literature [7–9,11,12,26]. All activities in each system show a positive deviation from the ideal solution. Other thermodynamic properties, such as partial Gibbs free energies, partial enthalpies, and Table 4 Zn potential as a function of temperature in the Zn/Zn2+ /Sn–Zn system
Fig. 2. In the Sn/Sn2+ /Sn–90 at.%Bi system: (a) potential vs. time, (b) temperature vs. time and (c) potential vs. temperature.
Five different Sn–Zn alloys are prepared and their compositions are listed in Table 2. Fig. 4(a) and (b) shows the determined potential and furnace temperature versus reaction time of the Zn/Zn2+ /Sn–20 at.%Zn, respectively. With similar procedures, the relationship between the potential and the reaction temperature can be determined as shown in Fig. 4(c). Similar linear relationships are observed for the Sn–Zn alloys of different compositions and the results are summarized in Table 4 and Fig. 5. Eight Sn–Bi–Zn alloys were prepared. Similar linear relationship between the Zn potential and temperature from the EMF results are found, and the results are shown in Figs. 6 and 7 and Table 5. The partial free energies, activities, and partial enthalpies can then be determined from the measured potential versus reaction temperature relationship. The following equations are the thermo-
No.
xZn
A (mV)
9 10 11 12 13
0.149 0.20 0.30 0.40 0.50
−43.852 −42.043 −34.491 −28.286 −18.788
B (mV/K) ± ± ± ± ±
1.326 0.546 0.404 0.545 1.173
0.1139 0.0994 0.0755 0.0594 0.0381
± ± ± ± ±
0.0017 0.0007 0.0005 0.0007 0.0015
Table 5 Zn potential as a function of temperature in the Zn/Zn2+ /Sn–Bi–Zn system No.
xSn
xBi
xZn
A (mV)
B (mV/K)
14 15 16
0.847 0.70 0.10
0.016 0.20 0.60
0.137 0.10 0.30
−45.062 ± 0.958 −49.981 ± 1.620 −43.910 ± 0.673
0.1174 ± 0.0012 0.1322 ± 0.0021 0.0736 ± 0.0009
No.
xZn
A (mV)
xSn /xBi = 1/1 17 18 19 20 21
0.10 0.20 0.30 0.40 0.50
−50.367 −44.545 −37.519 −30.731 −22.885
B (mV/K) ± ± ± ± ±
0.751 0.563 0.813 0.190 0.475
0.1270 0.0942 0.0718 0.0546 0.0376
± ± ± ± ±
0.0010 0.0007 0.0010 0.0002 0.0006
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small amount of Sn and Zn solubility. The composition of dark phase is Sn–0.2 at.%Bi–99.7 at.%Zn, and is the Zn phase with almost no Sn and Bi. The remaining is a fine-structure region composed of various phases, and its average composition is Sn–32.0 at.%Bi–10.5 at.%Zn. This fine-structure phase region is likely the liquid phase at 160 ◦ C prior to its removal from the furnace. Three different phases can be found in the fine-structure phase region, and they are the Bi, Zn and Sn phases based on the elemental X-ray mapping. Since the liquid phase region is in fact composed of different phases, the compositions vary locally, and thus the uncertainty in the liquid composition measurement is high. Fig. 9(b) is the XRD pattern of alloy no. 26, in which the characteristic peaks of Sn, Bi, and Zn phases are found. The XRD results agree with the microstructural analysis data. The equilibrium phases of alloy no. 26 are Bi, Zn and liquid phases at 160 ◦ C, and the liquid phase transforms into Sn, Bi and Zn phases when it is quenched to the room temperature. Similar results are found for alloy no. 28, and all these alloys are in the Bi–Zn-liquid three-phase tie-triangle region. Fig. 10(a) is the BEI micrograph of alloy no. 29 (Sn–15 at.%Bi–30 at.%Zn) annealed at 160 ◦ C, and it has three different phase regions. The composition of the largest and grey phase is Sn–7.6 at.%Bi–1.9 at.%Zn and is the Sn phase. The composition of the darkest phase is Sn–97.0 at.%Zn and is the Zn phase. The remaining phase region is composed of various phases and its average composition is Sn–25.0 at.%Bi–10.9 at.%Zn. Similar to the fine-structure phase region in the alloy no. 26, this phase region was the liquid phase prior to quenching. The XRD pattern of alloy no. 29 is shown in Fig. 10(b), and the diffraction peaks of Sn, Zn, and Bi phases are observed. The alloy no. 29 is in the Sn–Zn–liquid tie-triangle at 160 ◦ C. Similar results are found for alloy no. 27, and it is also in the Sn–Zn–liquid tie-triangle at 160 ◦ C. Fig. 11 is the BEI micrograph of alloy no. 22 (Sn–60 at.%Bi–2.5 at.%Zn) annealed at 160 ◦ C, and there are two phase regions. As listed in Table 7, the composition of the bright phase determined by EDS is Sn–96.3 at.%Bi–0.21 at.%Zn (Bi phase). The other phase region is composed of three phases. Similar to those mentioned above, it was the liquid phase at 160 ◦ C. The alloy no. 22 is in the Bi-liquid two-phase region at 160 ◦ C. Fig. 12 shows the BEI micrograph of alloy no. 23 (Sn–22.5 at.%Bi–2.5 at.%Zn) equilibrated at 160 ◦ C. The composition of the darker phase is Sn–5.0 at.%Bi–0.5 at.%Zn and is the Sn phase. The brighter phase region has various phases and its average composition is Sn–27.0 at.%Bi–3.0 at.%Zn and was the liquid phase at 160 ◦ C. Alloy no. 23 is in the Sn–liquid two-phase region. Fig. 13
Fig. 4. In the Zn/Zn2+ /Sn–20 at.%Zn system: (a) potential vs. time, (b) temperature vs. time and (c) potential vs. temperature.
partial entropies, are also determined in this study as can be seen in Table 6. 3.2. Phase equilibria Eight alloys were prepared and annealed at 160 ◦ C, and their compositions are shown in Table 7. As shown in Fig. 9(a), three-phase regions can be observed in the BEI (backscattered electron image) micrograph of alloy no. 26 (Sn–70 at.%Bi–10 at.%Zn) annealed at 160 ◦ C. The larger and brighter phase has a composition of Sn–98.6 at.%Bi–0.8 at.%Zn, and probably is the Bi phase with
Fig. 5. The relationship between potential and temperature of Sn–Zn alloys.
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Table 6 Partial molar properties of Sn–Bi, Sn–Zn and Sn–Bi–Zn alloys No.
xSn
GSn (J mole−1 )
aSn
H Sn (J mole−1 )
S Sn (J mole−1 K−1 )
◦
Partial molar properties of Sn in Sn–Bi alloys at 300 C (573 K) 1 0.10 0.1216 −10037 224 17.9 2 0.20 0.2342 −6915 382 12.7 3 0.30 0.3328 −5241 210 9.5 4 0.40 0.4384 −3929 151 7.1 5 0.50 0.5402 −2934 162 5.4 6 0.57 0.5932 −2488 431 5.1 7 0.60 0.6631 −1957 718 4.7 8 0.70 0.7292 −1613 −54 2.7 No.
GZn (J mole−1 )
aZn
xZn
H Zn (J mole−1 )
S Zn (J mole−1 K−1 )
◦
Partial molar properties of Zn in Sn–Zn alloys at 440 C (713 K) 9 0.149 0.2964 −7209 8462 10 0.20 0.3912 −5563 8113 11 0.30 0.5328 −3732 6656 12 0.40 0.6326 −2714 5458 13 0.50 0.7613 −1617 3626 No.
GZn (J mole−1 )
aZn
xZn
H Zn (J mole−1 )
22.0 19.2 14.6 11.5 7.4 S Zn (J mole−1 K−1 )
◦
Partial molar properties of Zn in Sn–Bi–Zn alloys at 440 C (713 K) 14 0.137 0.2842 −7457 8696 22.7 15 0.10 0.2366 −8544 9645 25.5 16 0.30 0.7566 −1653 8473 14.2 No. xZn
GZn (J mole−1 ) H Zn (J mole−1 ) S Zn (J mole−1 K−1 )
aZn
Partial molar properties of Zn in Sn–Bi–Zn alloys at 440 ◦ C (713 K) xSn /xBi = 1/1 17 0.10 0.2703−7754 9719 24.5 18 0.20 0.4789−4365 8596 18.2 19 0.30 0.6407−2639 7240 13.9 20 0.40 0.7657−1582 5930 10.5 21 0.50 0.8801 −757 4416 7.3
Table 7 Phase equilibria of Sn–Bi–Zn alloys at 160 ◦ C No.
Nominal composition xSn
xBi
Equilibrium Phases
xZn
Compositions xSn
xZn
xBi
0.025
L Bi
0.623 0.016
0.013 0.021
0.364 0.963
0.75
0.225 0.025
L Sn
0.7 0.945
0.03 0.005
0.27 0.05
24
0.45
0.45
0.10
L Zn
0.499 0.007
0.084 0.992
0.417 0.001
25
0.6
0.30
0.10
L Zn
0.683 0.005
0.039 0.995
0.278 0
26
0.2
0.7
0.10
L Bi Zn
0.575 0.006 0.001
0.105 0.008 0.997
0.32 0.986 0.002
27
0.75
0.15
0.10
L Sn Zn
0.652 0.892 0.015
0.097 0.024 0.981
0.251 0.084 0.004
28
0.30
0.40
0.30
L Bi Zn
0.579 0 0.005
0.097 0.016 0.99
0.324 0.984 0.005
29
0.55
0.15
0.30
L Sn Zn
0.641 0.905 0.03
0.109 0.019 0.97
0.25 0.076 0
22
0.375 0.60
23
Note. The uncertainty of the liquid composition is high. Segregation occurs and various solid phases form in the liquid phase region when the sample is removed from the furnace, and thus regional variation of composition in the originally liquid phase region is high.
Fig. 6. In the Zn/Zn2+ /Sn–20 at.%Bi–10 at.%Zn system: (a) potential vs. time, (b) temperature vs. time and (c) potential vs. temperature.
is the 160 ◦ C isothermal section of the Sn–Bi–Zn ternary system based on the experimental analyses of the ten equilibrated alloys. No ternary compound is found, and there are two three-phase regions, Bi–Zn–Liquid and Sn–Zn–Liquid, in the ternary system at 160 ◦ C. 3.3. Thermodynamic modeling Thermodynamic models of the three constituent binary systems, Sn–Zn, Sn–Bi and Bi–Zn are needed for the calculation of the Sn–Bi–Zn phase equilibria using the CALPHAD approach. The
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parameters of the Bi–Zn system assessed by Malakhov [10] are used directly. Thermodynamic parameters for the phases in the Sn–Zn, Sn–Bi and Sn–Bi–Zn systems were optimized using ThermoCalc [32] and Pandat software [33]. There are liquid, Sn (BCT A5), Bi (Rhombohedral A7) and practically pure Zn (HCP ZN) phases, and no binary and ternary compounds. The Gibbs free energies of the pure elements Sn, Bi and Zn are taken from the SGTE database [34]. Since the solubility in Zn phase is very small, it is treated as pure element in this study. Gibbs free energies of mixing for each solution phase, i.e. liquid, Sn (BCT A5) and Bi (Rhombohedral A7), are described by the following equation: Gm (T ) =
xi Gi0 (T ) + RT
i
xi ln xi
i
Fig. 7. The relationship between potential and temperature of Sn–Bi–Zn alloys.
+
i
j>i
xi xj
v
Lij (xi − xj )
v
v
Fig. 8. (a) Activities of Sn in Sn–Bi alloys, (b) activities of Zn in Sn–Zn alloys and (c) activities of Zn in Sn–Bi–Zn alloys.
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Fig. 11. BEI micrograph of alloy no. 22 (Sn–60 at.%Bi–2.5 at.%Zn) annealed at 160 ◦ C for 10 weeks.
Fig. 9. (a) BEI micrograph of alloy no. 26 (Sn–70 at.%Bi–10 at.%Zn) annealed at 160 ◦ C for 15 weeks and (b) XRD pattern of alloy no. 26 annealed at 160 ◦ C for 15 weeks.
Fig. 12. BEI micrograph of alloy no. 23 (Sn–22.5 at.%Bi–2.5 at.%Zn) annealed at 160 ◦ C for 10 weeks.
Fig. 10. (a) BEI micrograph of alloy no. 29 (Sn–15 at.%Bi–30 at.%Zn) annealed at 160 ◦ C for 15 weeks and (b) XRD pattern of alloy no. 29 annealed at 160 ◦ C for 15 weeks.
Fig. 13. Isothermal section of the Sn–Bi–Zn ternary system at 160 ◦ C.
C.-f. Yang et al. / Materials Chemistry and Physics 112 (2008) 94–103 Table 8 Thermodynamic parameters of the Sn–Bi–Zn system System
Parameters
Sn–Bi
0 liq LBiSn = 575.3621+1.2470T 1 liq LBiSn = −27.1141 − 0.2695T 0 BCT A5 LBiSn = 2340.9429 − 1.0836T 1 BCT A5 LBiSn = −3.096.9418 0 Rhombohedral A7 LBiSn = 20574.8595 − 22.6000T 0 Rhombohedral A7 LBiSn = −5769.0000 + 14.7401T
Sn–Zn
0 liq LSnZn = 21468.89 − 100.79T + 12.00T ln T 1 liq LSnZn = −6355.40 + 12.38T − 1.12T ln T ) 2 liq LSnZn = 2624.86 − 1.52T 0 HCP Zn LSnZn = 4941.62 + 5.00T 0 BCT A5 LSnZn = 6772.15 + 24.15T
Bi–Zn
0 liq LBiZn = 18265.09 − 8.6763T 1 liq LBiZn = −6061.21 + 0.79581T 2 liq LBiZn = −6422.6 + 11.71966T 3 liq LBiZn = 7227.44 − 9.2905T 4 liq LBiZn = 21123.07 − 27.14705T 5 liq LBiZn = −20747.56 + 22.01759T 6 liq LBiZn = −7600.36 + 13.15957T 0 HCP Zn LBiZn = 25,000 0 Rhombohedral A7 LBiZn = 10, 000
Sn–Bi–Zn
0 liq LBiSnZn 1 liq LBiSnZn 3 liq LBiSnZn
= −39083.23 + 34.81T = −5617.41 + 6.73T = 2.737.35 − 2.48T
where Gi0 is the molar Gibbs free energy of pure tin, bismuth, or zinc, xi is the molar fraction of the component “i”, R is the gas constant, and T is the absolute temperature. Interaction parameter of the solution v Lij is given by the following equation: v
Lij = Av + Bv T + Cv T ln T
Thermochemical and phase equilibria data obtained from the literature [7–27] and this study are used for optimization.
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Table 9 Experimental and calculated ternary eutectic point
Experiment [24] This work Malakhov [23] Moelans [22]
T [◦ C]
xBi
xSn
135 ± 0.5 135.9 130 132
0.41 0.39 0.39 0.36
0.57 0.56 0.54 0.58
The thermodynamic parameters determined are summarized in Table 8. The calculated activities of Zn in the Sn–Zn system are superimposed with the experimental data as shown in Fig. 8(b), and are in good agreement with the experimental data [9,11,12]. Fig. 14(a) shows the molar enthalpy of mixing of the Sn–Zn liquid phase. Previous optimization of the Sn–Zn system was done by Ohtani et al. [13] where the enthalpy of mixing was described without temperature dependency. A temperature-dependent model is used to describe the enthalpy of mixing in this study. As shown in Fig. 14(a), the calculated enthalpies of mixing at 433 and 525 ◦ C are in good agreement with the experimental results [14–16], and the agreement is better than that of the previous modeling results [13]. Fig. 14(b) shows the Sn–Zn phase diagram. The eutectic temperature is at 199.1 ◦ C. As can be seen in Fig. 14(b), the calculated liquidus and phase boundaries are in agreement with the experimental boundary data [9,12,17,18]. Similar to those in the Sn–Zn binary system, the activities of Sn in Sn–Bi system, partial enthalpies of mixing of liquid phase of the Sn–Bi system, and the Sn–Bi phase diagram are shown in Figs. 8(a) and 15(a) and (b), respectively. The eutectic temperature is at 139.9 ◦ C, and the calculated thermodynamic properties and phase equilibria are in good agreement with the experimental results [7,8,19–22]. The activities of zinc and the enthalpies of mixing of the liquid phase in the ternary Sn–Bi–Zn system are shown in Figs. 8(c) and 16(a) and (b). The calculated results obtained in this study and the previous optimizations [23,24] all are in good agreement with the experimental data [25,26]. Fig. 16(c) is the isopleth in Sn–Bi–Zn system at a constant fraction of Zinc equal to 0.05 mole fraction. Compared with the previous modeling results [23,24], the calculated boundary of this study very well fit to the experimental
Fig. 14. (a) Enthalpy of mixing in the binary Sn–Zn system and (b) phase diagram of the Sn–Zn system.
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Fig. 15. (a) Partial enthalpy of mixing in the binary Sn–Bi system and (b) phase diagram of Sn–Bi system.
Fig. 16. (a) Activity of Zn in the ternary Sn–Bi–Zn system at xZn = 0.2, (b) enthalpy of mixing in the ternary Sn–Bi–Zn system at xSn /xZn = 3/7 and (c) isoplethal section of the ternary Sn–Bi–Zn system at xZn = 0.05.
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equilibria data determined in this study and those in the literatures, the thermodynamic models of the Sn–Bi–Zn ternary system have been successfully assessed. In the ternary Sn–Bi–Zn system, there are two tie-triangles, liquid + Bi + Zn and liquid + Sn + Zn, at 160 ◦ C, and there is one invariant reaction, liquid = Sn + Bi + Sn, at 135.9 ◦ C and Sn–39 at.%Bi–5 at.%Zn Acknowledgements The authors acknowledge the financial support from the National Science Council of Taiwan (NSC 95-2218-E-007-028). Authors also are grateful to the National Center for Highperformance Computing for the use of PANDAT software. References
Fig. 17. Liquidus projection of Sn–Bi–Zn system.
solidus line [25], while the earlier studies reported a slightly lower temperature [25,26]. The calculated 160 ◦ C isothermal section is shown in Fig. 13. The phase relationships determined from the calculation are in agreement with experimental data. The calculated composition of Bi phase at 160 ◦ C equals xBi = 0.974, xSn = 0.017, xZn = 0.008, and is consistent with the experimental data of this study. Braga et al. [27] determined the Sn–Bi–Zn isothermal section at 100 ◦ C, and they report a much higher Zn solubility of 3.7 wt.% Zn. According to the Bi–Zn binary system [10], the Zn solubility in Bi is 0.4 at.% at 100 ◦ C and 0.9 at.% at 160 ◦ C. Braga et al. [27] had also found the solubility of Zn in Bi phase to be 0.3 wt.% ± 0.1 at 200 ◦ C. Although the addition of Sn might alter the solubility of Zn in Bi, it is still very unlikely if it could make such dramatic difference. Considering those inconsistencies, the data of Braga et al. [27] were not taken into consideration in the modeling processes. The calculated liquids projection is shown in Fig. 17. The ternary eutectic point was experimentally determined by Luef [25] at 135 ◦ C and Sn–41 at.%Bi–2 at.%Zn. The calculated result of this study confirms that it is a type I reaction, liquid = Sn + Bi + Zn, at 135.9 ◦ C and Sn–39 at.%Bi–5 at.%Zn. As summarized in Table 9, the calculated results determined in this study are in better agreement than those modeling results reported previously [23,24]. 4. Conclusions There are no binary and ternary compounds found in the Sn–Bi–Zn system at 160 ◦ C. Based on the thermodynamic and phase
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