Phase equilibria of Sn–Sb–Cu system

Materials Chemistry and Physics 132 (2012) 703–715

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Phase equilibria of Sn–Sb–Cu system Sinn-wen Chen a,∗ , An-ren Zi a , Wojciech Gierlotka b , Ching-feng Yang a , Chao-hong Wang c , Shih-kang Lin a,d , Chia-ming Hsu a a

Department of Chemical Engineering, National Tsing Hua University, Hsin-Chu, Taiwan Department of Chemical Engineering & Materials Science, Yuan Ze University, Chung-Li, Taiwan Department of Chemical Engineering, National Chung Cheng University, Chia-Yi, Taiwan d Department of Materials Science and Engineering, National Cheng Kung University, Tainan, Taiwan b c

a r t i c l e

i n f o

Article history: Received 4 September 2011 Received in revised form 7 November 2011 Accepted 30 November 2011 Keywords: Alloys Phase equilibria Thermodynamic properties Computer modeling and simulation

a b s t r a c t Ternary Sn–Sb–Cu alloys are prepared. The primary solidification phases, the phase transformation temperatures, and the equilibrium phases at 250 ◦ C are experimentally determined. The liquidus projection and the 250 ◦ C phase equilibria isothermal section of the Sn–Sb–Cu system are proposed based on the experimental results and the phase diagrams of the three constituent binary systems. Using the CALPHAD approach, thermodynamic modeling of the Sn–Sb–Cu ternary system is carried out based on the experimental information determined in this study and those in the literatures, together with the developed thermodynamic models of the three constituent binary systems. The liquidus projection and the isothermal sections are then calculated using the models developed in this study and the results are in good agreement with experimental determinations. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Soldering is the most frequently used joining technology in the electronic industry. Some electronic products require even more than one soldering process during their manufacturing. To prevent re-melting of the earlier joints in the later soldering processes of different steps, solders with different melting points are used. Sn–Sb and Sn–Sb–Cu-based alloys have been developed as high temperature solders [1–4], and Cu substrates and surface finishes are frequently encountered in electronic products. Thus knowledge of phase equilibria of the Sn–Sb–Cu ternary system is valuable for the applications and development of Sn–Sb and Sn–Sb–Cu-based solders. Although phase equilibria of Sn–Sb–Cu had been experimentally examined since 1913 [5] due to the early engineering interests of Sn–Sb–Cu alloys as bearing metal and others, there are only few experimental studies available [4–11]. Moreover, the reported phase boundaries and ternary compound formation are not consistent. There is also no available thermodynamic modeling of the Sn–Sb–Cu system. Liu et al. [12] showed a calculated Sn–Sb–Cu liquidus projection but without releasing their thermodynamic models and parameters, and their calculated types of the invariant reactions are different from the experimental determinations [9].

∗ Corresponding author. Tel.: +886 3 5721734; fax: +886 3 5715408. E-mail address: [email protected] (S.-w. Chen). 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.11.088

This study experimentally determines the 250 ◦ C phase equilibria isothermal section and the liquidus projection of the Sn–Sb–Cu system. The CALPHAD [13] approach is used to thermodynamically model the Sn–Sb–Cu system based on the ternary experimental phase equilibria results, thermodynamic properties of Sn–Sb–Cu alloys [14,15], and the thermodynamic models of the three binary constituent systems [16–18]. The invariant reactions, the liquidus projection, and the 250 ◦ C isothermal section of the Sn–Sb–Cu system are then calculated using the determined thermodynamic models. 2. Experimental determinations 2.1. Experimental procedures Ternary Sn–Sb–Cu alloys were prepared with pure Sn shots (99.985%, Showa, Tokyo, Japan), Sb shots (99.999%, Sigma Aldrich, St. Louis, MO, USA) and Cu shots (99.99%, Sigma Aldrich, St. Louis, MO, USA). Proper amounts of the constituent elements were weighed and encapsulated in a quartz tube in 2 × 10−5 bar vacuum. The sample capsule was placed in a furnace at 1000 ◦ C for 3 days, until the elements were molten and completely mixed. The sample capsule was then quenched in water. The quenched ingots were weighed with no noticeable weight change, and they were used for phase equilibria and liquidus projection determinations. For the phase equilibria study, the quenched samples were equilibrated in a furnace at 250 ◦ C. Depending upon the lengths of time the alloys would take to reach phase equilibrium, the annealing

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Fig. 1. (a) BEI micrograph of alloy #5 (Sn–3.0 at.%Sb–37.0 at.%Cu), (b) BEI micrograph of alloy #07 (Sn–10.0 at.%Sb–40.0 at.%Cu), (c) BEI micrograph of alloy #10 (Sn–15.0 at.%Sb–40.0 at.%Cu), (d) BEI micrograph of alloy #15 (Sn–10.0 at.%Sb–60.0 at.%Cu), (e) BEI micrograph of alloy #13 (Sn–30.0 at.%Sb–35.0 at.%Cu), (f) BEI micrograph of alloy #19 (Sn–40.0 at.%Sb–45.0 at.%Cu), (g) SEI micrograph of alloy #18 (Sn–60.0 at.%Sb–20.0 at.%Cu), (h) BEI micrograph of alloy #24 (Sn–90.0 at.%Sb–5.0 at.%Cu), (i) BEI micrograph of alloy #26 (Sn–22.0 at.%Sb–75.0 at.%Cu), and (j) BEI micrograph of alloy #27 (Sn–12.0 at.%Sb–85.0 at.%Cu).

times varied from 2 to 14 months. For the liquidus projection study, the alloy was heated up to 50 degrees higher than its liquidus temperature, cooled down in a furnace to 10 degrees lower than its solidus temperature, and then quenched in water. The cooling rate was about 20 ◦ C min−1 . The as-solidified alloy samples were used for the determination of primary solidification phases. Since primary solidification phases are the first phase formed during solidification, their sizes are usually larger and sometimes are with dendritic structures, and usually can be distinguished from their microstructures [19]. The liquidus and solidus temperatures were determined from the differential thermal analysis (DTA, Perkin

Elmer DA7) measurements. The scanning rates of the DTA experiments were 5 and 10 ◦ C min−1 . The equilibrated and the as-solidified alloy samples were cut into half. One part was ground into powders for X-ray diffraction analysis (XRD, Scintac, XDS-2000V/H, USA), and the other part was metallographically analyzed. The samples were mounted in epoxy, grounded with SiC sandpapers of different grades, and finally polished with alumina slurry. Microstructures were examined using optical microscope (Olympus, BH, Japan) and scanning electron microscope (SEM, JEOL, S-2500, Japan). The compositions of the phases were determined using electron probe

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Fig. 2. (a) XRD pattern of alloy #5 annealed at 250 ◦ C and (b) XRD pattern of alloy #7 annealed at 250 ◦ C.

microanalysis (EPMA, JEOL, JXA8600 SX, Japan). Thestandard specimens used were pure Sn, Sb and Cu elements. 3. Results and discussion 3.1. Sn–Sb–Cu isothermal section at 250 ◦ C Fig. 1(a) is the backscattered electron image (BEI) micrograph of alloy #5 (Sn–3.0 at.%Sb–37.0 at.%Cu), as summarized in Table 1, equilibrated at 250 ◦ C for 2 months. Two different phase regions are observed. The composition of the darker phase region is Sn–1.0 at.%Sb–53.3 at.%Cu, and that of the brighter continuous matrix is Sn–12.3 at.%Sb. According to its compositions and the available binary phase diagram information, it is presumed that the dark phase is the ␩-Cu6 Sn5 phase with 1.0 at.% Sb solubility. The brighter matrix phase was the liquid phase at 250 ◦ C, which solidified when the sample was removed from the furnace. Fig. 2(a) is the X-ray diffractogram of alloy #5. The diffraction results are in agreement with compositional determinations that the alloy #5 at 250 ◦ C is in the liquid + ␩-Cu6 Sn5 two-phase field. As shown in Fig. 1(a), the fraction of Cu6 Sn5 phase is about 65%, and that of liquid phase region is about 35%. The results are consistent with the basic requirement of mass balance. As summarized in Table 1, similar results are found for alloys #1 (Sn–5.0 at.%Sb–5.0 at.%Cu) and #2 (Sn–3.0 at.%Sb–17.0 at.%Cu), and they are in the liquid + ␩-Cu6 Sn5 two-phase field. Fig. 1(b) is the BEI micrograph of the alloy #7 (Sn–10.0 at.%Sb–40.0 at.%Cu) equilibrated at 250 ◦ C for 3 months showing three different phase regions. Following similar analytical procedures, it can be concluded the alloy is in the ␩-Cu6 Sn5 + Sn3 Sb2 + liquid three-phase region. The dark phase is the ␩-Cu6 Sn5 phase, the homogeneous bright phase is the Sn3 Sb2 phase, and the bright phase region with dark precipitates was the liquid phase prior to quenching. Fig. 2(b) is the

Fig. 3. (a) Binary phase diagram of Cu–Sn system [16], (b) binary phase diagram of Sn–Sb system [17], and (c) binary phase diagram of Cu–Sb system [18].

X-ray diffractogram of alloy #7. The diffraction results are in agreement with compositional determinations that alloy #7 at 250 ◦ C is in the ␩-Cu6 Sn5 + Sn3 Sb2 + liquid three phase region. Similar results are found for alloys #3, 4, and 6, and they are all in the ␩-Cu6 Sn5 + Sn3 Sb2 + liquid three-phase region. It can also be noticed that the solubility of Cu in the Sn–Sb phases is very small. It is also noteworthy that lengths of annealing time vary with samples from 2 months to 14 months. The annealing time is

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Table 1 Equilibrium phases of the Sn–Sb–Cu alloys annealed at 250 ◦ C. Alloy #

Nominal composition

Equilibrium phases

Sn (at.%)

Sb (at.%)

Cu (at.%)

1

90

5

5

2

80

3

17

3

70

15

15

4

60

37

3

5

60

3

37

6

56

30

14

7

50

10

40

8

48

45

7

9

45

40

15

10

45

15

40

11

40

30

30

12

37

60

3

13

35

30

35

14

30

30

40

15

30

10

60

16

30

2

68

17

23

75

2

18

20

60

20

19

15

40

45

20

20

20

60

21

20

10

70

22

15

80

5

23

10

40

50

24

5

90

5

25

3

37

60

26

3

22

75

27

3

12

85

Sn(L) Cu6 Sn5 Sn(L) Cu6 Sn5 Sn(L) Cu6 Sn5 Sn3 Sb2 Sn(L) Cu6 Sn5 Sn3 Sb2 Sn(L) Cu6 Sn5 Sn(L) Cu6 Sn5 Sn3 Sb2 Sn(L) Cu6 Sn5 Sn3 Sb2 ␤(SnSb) Cu6 Sn5 ␤(SnSb) Cu6 Sn5 Cu3 Sn ␤(SnSb) Cu6 Sn5 ␤(SnSb) Cu6 Sn5 Cu3 Sn ␤(SnSb) Sb Cu2 Sb ␤(SnSb) Cu2 Sb Cu3 Sn ␤(SnSb) Cu2 Sb Cu3 Sn ␤(SnSb) Cu6 Sn5 Cu3 Sn Cu3 Sn Cu6 Sn5 ␤(SnSb) Sb Cu2 Sb ␤(SnSb) Sb Cu2 Sb ␤(SnSb) Cu2 Sb ␤(SnSb) Cu2 Sb Cu3 Sn ␤(SnSb) Cu2 Sb Cu3 Sn ␤(SnSb) Sb Cu2 Sb ␤(SnSb) Sb Cu2 Sb Cu2 Sb Sb ␤(SnSb) Sb Cu2 Sb Cu4 Sb Cu2 Sb Cu4 Sb Cu

Phase composition Sn (at.%)

Sb (at.%)

Cu (at.%)

95.2 45.6 96.6 45.8 86.4 42.9 58.3 86.3 45.5 57.8 87.7 45.7 85.5 44.3 56.7 88.3 44.3 57.0 46.1 33.6 48.8 34.5 24.3 55.7 38.8 49.7 35.2 24.3 41.3 11.9 3.2 46.3 6.6 23.2 47.3 6.9 23.3 48.9 36.0 22.2 24.1 41.0 41.6 8.5 3.3 41.7 9.4 2.1 38.4 2.1 45.7 5.4 18.4 43.7 5.2 18.3 40.8 5.7 3.9 41.5 13.3 1.6 2.9 9.1 39.2 8.8 0.9 2.7 2.8 3.1 1.5

4.8 0.7 3.3 0.5 13.4 3.7 41.6 13.6 1.7 42.2 12.3 1.0 14.0 1.9 43.1 10.5 1.6 42.7 53.8 13.1 51.1 12.4 1.4 43.7 7.1 49.5 11.7 0.9 58.7 87.7 31.7 53.0 27.2 2.1 51.2 27.3 2.2 47.7 10.1 4.3 0.9 4.5 58.1 91.5 30.6 58.1 90.0 32.0 60.4 31.4 52.0 27.3 6.9 50.2 27.8 7.1 58.7 94.1 31.0 58.0 85.6 31.8 31.4 90.6 57.0 87.5 32.8 20.1 30.0 16.7 3.3

0.0 53.7 0.1 53.7 0.2 53.4 0.1 0.1 52.8 0.0 0.0 53.3 0.5 53.8 0.2 1.2 54.1 0.3 0.1 53.4 0.1 53.1 74.3 0.6 54.1 0.8 53.1 74.8 0.0 0.4 65.1 0.7 66.2 74.7 1.5 66.0 74.5 3.4 53.9 73.5 75.0 54.5 0.3 0.0 66.1 0.2 0.6 65.9 1.2 66.5 2.3 67.3 74.7 6.1 67.0 74.6 0.5 0.2 65.1 0.5 1.1 66.6 65.7 0.3 3.8 3.7 66.3 77.2 67.2 80.2 95.2

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Fig. 4. Experimental isothermal section of Sn–Sb–Cu ternary system superimposed with the alloys examined in this study at 250 ◦ C.

2–3 months, for alloys in the Sn-rich corner, 6 months for alloys in the Sb-rich corner, and14 months for alloys in the Cu-rich corner. Fig. 1(c)–(j) are the micrographs of alloys #10 (Sn–15.0 at.%Sb–40.0 at.%Cu), #15 (Sn–10.0 at.%Sb–60.0 at.%Cu),

707

(Sn–30.0 at.%Sb–35.0 at.%Cu), #19 (Sn–40.0 at.%Sb– #13 45.0 at.%Cu), #18 (Sn–60.0 at.%Sb–20.0 at.%Cu), #24 (Sn–90.0 at.%Sb –5.0 at.%Cu), #26 (Sn–22.0 at.%Sb–75.0 at.%Cu), and #27 (Sn– 12.0 at.%Sb–85.0 at.%Cu), respectively. They are representative alloys from different phase regions and are in the ␤-SnSb + ␩-Cu6 Sn5 , ␤-SnSb + ␩-Cu6 Sn5 + ␧-Cu3 Sn, ␤-SnSb + ␩Cu2 Sb + ␧-Cu3 Sn, ␤-SnSb + ␩-Cu2 Sb, ␤-SnSb + Sb + ␩-Cu2 Sb, ␩-Cu2 Sb + Sb, ␦-Cu4 Sb + ␩-Cu2 Sb, and ␦-Cu4 Sb + Cu, respectively. Tasaki [9] reported the formation of a ternary compound Sn7 Sb3 Cu12 . Lee et al. [10] did not find any ternary compound, but they reported a ␩-Cu6 Sn5 phase with 6 at.% Sb solubility instead. EPMA analysis of alloy #15, as summarized in Table 1, indicates that the Sb solubility in the ␩-Cu6 Sn5 phase is 11 at.% in this study, similar to that found by Lee et al. [10]. Since there is no existing evidence of the ternary compound and significant solubility of the tertiary element in the ␩-Cu6 Sn5 has been previously observed in the Sn–Cu–Ni system [19,20], a ␩-Cu6 Sn5 phase with 11 at.% Sb solubility is proposed instead of the existence of a ternary phase. Gunzel and Schubert [11] reported the formation of a ternary ␬ phase in the Cu-rich corner; however, there is no X-ray diffraction data of the ␬ phase. Lee et al. [10] indicated a continuous solid solution between the ␧-Cu3 Sn and ␦-Cu4 Sb phases. Blalock et al. [21] presented a review of the Sn–Sb–Cu system, but did not comment on the differences. No ternary compound or a continuous solid solution is observed in the Cu-rich corner in this study. The ␧-Cu3 Sn phase has a oC80 crystal structure with space group of Cmcm [22], while the ␦-Cu4 Sb phase has the hp crystal structure with space

Fig. 5. (a) BEI micrograph of alloy #14 (Sn–25.0 at.%Sb–35.0 at.%Cu), (b) BEI micrograph of alloy #3 (Sn–5.0 at.%Sb–10.0 at.%Cu), (c) Optical micrograph of alloy #01 (Sn–2.5 at.%Sb–2.5 at.%Cu), (d) SEI micrograph of alloy #2 (Sn–15.0 at.%Sb–2.0 at.%Cu), (e) BEI micrograph of alloy #7 (Sn–39.0 at.%Sb–1.0 at.%Cu), (f) BEI micrograph of alloy #23 (Sn–70.0 at.%Sb–10.0 at.%Cu), (g) BEI micrograph of alloy #13 (Sn–35.0 at.%Sb–25.0 at.%Cu), (h) BEI micrograph of alloy #31 (Sn–35.0 at.%Sb–63.0 at.%Cu), and (i) BEI micrograph of alloy #32 (Sn–5.0 at.%Sb–90.0 at.%Cu).

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group of P63 /mmc [23]. Since they have different crystal structures, it is impossible for the ␧-Cu3 Sn and ␦-Cu4 Sb phases to form a continuous solid solution. This information and the ␦-Cu4 Sb + ␩-Cu2 Sb two-phase region found for alloy #26 indicated the likely existence of a three-phase region, ␧-Cu3 Sn + ␦-Cu4 Sb + ␩-Cu2 Sb. With the existence of this three-phase region, there should also be a two-phase region, ␧-Cu3 Sn + ␦-Cu4 Sb, between the ␧-Cu3 Sn and ␦-Cu4 Sb phases. Based on the experimental results mentioned above and the phase diagrams of the three binary systems shown in Fig. 3(a)–(c) [16–18], the 250 ◦ C isothermal section of the Sn–Sb–Cu ternary system is proposed, as shown in Fig. 4. There are seven tie-triangles, L + Sn3 Sb2 + ␩-Cu6 Sn5 , ␤-SnSb + ␧-Cu3 Sn + ␩-Cu6 Sn5 , Sn3 Sb2 + ␤-SnSb + ␩-Cu6 Sn5 , ␤-SnSb + ␩-Cu2 Sb + ␧-Cu3 Sn,␤-SnSb + Sb + ␩-Cu2 Sb, ␩-Cu2 Sb + ␦Cu4 Sb + ␧-Cu3 Sn, and ␦-Cu4 Sb + Cu + ␧-Cu3 Sn. No ternary compound is found in this study at 250 ◦ C. Although there is no sample in the thin Sn3 Sb2 + ␩-Cu6 Sn5 , ␤-SnSb + ␧-Cu3 Sn, ␩Cu2 Sb + ␧-Cu3 Sn, and ␦-Cu4 Sb + ␧-Cu3 Sn region, the existence of these two-phase regions can be justified from the two adjacent tie-triangles. 3.2. Liquidus projection Fig. 5(a) is the BEI micrograph of as-solidified alloy #14 (Sn–25.0 at.%Sb–35.0 at.%Cu). The dark needle-shape phase is the primary solidification phase. As shown in Table 2, its composition is Sn–5.5 at.%Sb–75.1 at.%Cu, which is the ␧-Cu3 Sn phase. Since the liquidus valley delineates the boundaries of different primary solidification phases [24,25], the results of primary solidification phases in the as-solidified Sn–Sb–Cu alloys can be used to construct the lines of the liquidus valley. However, the temperature descending directions of these lines and the temperatures of the invariant reactions need to be determined by separate thermal analysis experiments. As mentioned above, the primary solidification phase is the first phase to come out of the liquid phase, and larger size and dendritic structure are usually characteristics of the primary solidification phase. In addition, the primary solidification phase is a good nucleation site for the following solidification phases, and thus the secondary solidification phase would be usually found on both sides of the primary solidification phase. However, it should be mentioned that if significant solid state phase transformation occurs or the composition of the alloy is close to the twofold saturation of the liquidus projection, it might be difficult to identify the primary solidification phase. Other experimental techniques, such as directional solidification, would be effective to overcome these difficulties. Fig. 5(b)–(j) are the micrographs of alloys #3 (Sn– 5.0 at.%Sb–10.0 at.%Cu), #1 (Sn–2.5 at.%Sb–2.5 at.%Cu), #2 (Sn– 15.0 at.%Sb–2.0 at.%Cu), #7 (Sn–39.0 at.%Sb–1.0 at.%Cu), #23 (Sn–70.0 at.%Sb–10.0 at.%Cu), #13 (Sn–35.0 at.%Sb–25.0 at.%Cu), #31 (Sn–35.0 at.%Sb–63.0 at.%Cu), and #32 (Sn–5.0 at.%Sb– 90.0 at.%Cu), respectively. These are representative alloys from different primary solidification regions. As listed in Table 2, they are in the ␩-Cu6 Sn5 , Sn, Sn3 Sb2 , ␤-SnSb, Sb, ␩-Cu2 Sb, (␧-Cu3 Sb, Cu4 Sn), Cu primary solidification phase regions, respectively. Fewer alloy samples were prepared in the Cu-rich corner since there is less soldering interest and is more difficult in solidification sample preparation. There are no alloy samples prepared in the ␤-Cu17 Sn3 primary solidification phase region. Based on the experimental results and the phase diagrams of the constituent binary systems [17,22,23], different primary solidification phase regions are determined, as shown in Fig. 6. No ternary compound is found in this system. Ten primary solidification phases are determined in this system, which are ␧-Cu3 Sn,

Fig. 6. Liquidus projection of the Sn–Sb–Cu ternary system superimposed with the alloys examined in this study and reaction paths.

␩-Cu6 Sn5 , Sn, Sn3 Sb2 , ␤-SnSb, Sb, ␩-Cu2 Sb, (Cu3 Sb, Cu4 Sn), ␤Cu17 Sn3 , and Cu. It should be noted that there was no experimental examination of the ␤-Cu17 Sn3 phase. Its existence and its compositional regime as a primary solidification phase is constructed based on the presumption of the validity of the binary Cu–Sn phase relationship [16] and calculations using the ternary thermodynamic models. As summarized in Table 3, the compositions of the primary solidification phase (Cu3 Sb, Cu4 Sn), continuously change from the Cu4 Sn phase side to the ␧-Cu3 Sb phase side. Although the compositional homogeneity ranges of the two phases are different, the two phases have the cF16 crystal structure with the space group of ¯ [22,23]. Hence, they could form a continuous solid solution. Fm3m Fig. 7 is the DTA heating and cooling curves of alloy #16 (Sn–15.0 at.%Sb–45.0 at.%Cu), showing five reaction peaks with reaction temperatures of 553, 394, 348, 318 and 239 ◦ C. Since the undercooling effect is usually significant for cooling curves, the reaction temperatures reported in this study as summarized in Table 3 are determined from the heating curves [26–28]. The five reaction temperatures correspond to the five reactions, L → ␧Cu3 Sn at 553 ◦ C, the precipitation of the second solidification phase Cu6 Sn5 at 394 ◦ C, the precipitation of the third solidification phase SnSb at 348 ◦ C, L + ␤-SnSb = Sn3 Sb2 + ␩-Cu6 Sn5 at 318 ◦ C, and L + Sn3 Sb2 = Sn + ␩-Cu6 Sn5 at 239 ◦ C, respectively. It is interesting to notice that the solidification path does not follow the Cu3 Sn/Cu6 Sn5 liquidus line, and it cuts through the Cu6 Sn5 phase region instead.

Fig. 7. DTA heating and cooling curve of alloy #16 (Sn–15.0 at.%Sb–45.0 at.%Cu).

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Table 2 Primary solidification phases of the ternary Sn–Sb–Cu alloys. Alloy #

Nominal composition Sn (at.%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

95 83 85 80 70 70 60 50 50 50 45 43 40 40 40 40 35 30 30 25 25 25 20 20 15 15 17 12 8 5 2 5

Primary solidification phase

Sb (at.%) 2.5 15 5 5 25 7 39 45 35 10 40 27 35 25 20 15 45 20 15 50 25 3 70 45 65 25 5 23 32 43 35 5

Cu (at.%) 2.5 2 10 15 5 23 1 5 15 40 15 30 25 35 40 45 20 50 55 25 50 72 10 35 20 60 78 65 60 52 63 90

Sn Sn3 Sb2 Cu6 Sn5 Cu3 Sn ␤(SnSb) Cu3 Sn ␤(SnSb) ␤(SnSb) Cu6 Sn5 Cu3 Sn Cu2 Sb Cu3 Sn Cu2 Sb Cu3 Sn Cu3 Sn Cu3 Sn Cu2 Sb (Cu3 Sb,Cu4 Sn) (Cu3 Sb,Cu4 Sn) Cu2 Sb (Cu3 Sb,Cu4 Sn) (Cu3 Sb,Cu4 Sn) Sb Cu2 Sb Sb (Cu3 Sb,Cu4 Sn) (Cu3 Sb,Cu4 Sn) (Cu3 Sb,Cu4 Sn) (Cu3 Sb,Cu4 Sn) Cu2 Sb (Cu3 Sb,Cu4 Sn) Cu

This cross-over phenomenon is a result of mass-balance and has been discussed previously [29]. There are seven ternary invariant reactions in this system. Temperatures of all the ternary invariant reactions in the ternary Sn–Sb–Cu system are shown in Fig. 6 and summarized in Table 3. 4. Thermodynamic modeling 4.1. Modeling procedures The CALPHAD approach [13,30] is undertaken, using the commercial software packages, ThermoCalc [31] and Pandat [32], to optimize thermodynamic parameters and calculate phase diagrams. The primary effort is to develop thermodynamic modeling of the ternary Sn–Sb–Cu ternary system. Experimental data, such as the liquidus projection and the 250 ◦ C isothermal section determined in this study, the 260 ◦ C isothermal section, enthalpy of mixing of liquid phase [14] and activities of Sn in liquid phase [15] are included for the assessment. The three binary constituent systems have been evaluated, and the recently published thermodynamic descriptions of the three binary constituent systems, Cu–Sn, Sn–Sb, and Cu–Sb, [16–18] are adopted without remodeling.

Phase composition Sn (at.%)

Sb (at.%)

Cu (at.%)

97.1 55.6 44.6 25.3 53.2 24.4 52.5 39.1 27 23.9 4.3 19.3 4.8 19.4 20.8 23 2.7 18.7 21.5 1.7 13.7 22.8 6.6 3.0 5.6 9.2 18.4 9.3 3.4 0.8 0.7 4.1

2.9 44.4 1.4 0.3 46.8 0.8 47.4 60.8 20.6 1.4 29.6 6.0 28.6 5.5 5.0 2.8 31.1 10.4 4.3 31.2 17.3 2.2 93.4 30.8 94.4 21.2 5.8 21.2 27.0 32.6 24.4 2.5

0.0 0.0 54 74.4 0.0 74.8 0.1 0.1 52.4 74.7 66.1 74.7 66.6 75.1 74.2 74.2 66.2 70.9 74.2 67.1 69.0 75.0 0.0 66.2 0.0 69.6 75.8 69.5 69.6 66.6 74.9 93.4

The modeling includes determination of the thermodynamic models and the optimization of the thermodynamic parameters, and it is carried out step by step following the guideline by SchmidFetzer et al. [33]. Each piece of the selected information is given a certain weight-based on experiment accuracies. First, the thermodynamic parameters of the liquid phase are determined based on the experimental thermodynamic data. After that, descriptions of some binary phases (i.e. ␩-Cu6 Sn5 , ␧-Cu3 Sn) are changed to include the tertiary element, and then the ternary interaction parameters for solution phases are introduced to describe the ternary solubility of the solid phases. All of the parameters are finally optimized together to provide the best description of the ternary system.

4.2. Thermodynamic descriptions of phases The following phases are considered in this work: FCC A1(Cu), BCT A5(Sn), Rhombohedral A7(Sb), BCC A2(␤-Cu17 Sn3 ), LIQUID, ␨-Cu10 Sn3 , ␦-Cu41 Sn11 , ␩-Cu6 Sn5 , Sn3 Sb2 , ␥-Cu17 Sb3 , ␨-Cu10 Sb3 , ␩-Cu2 Sb, ␧-Cu3 Sb, Sn3 Sb2 , ␧-Cu3 Sn, GAMMA DO3 (Cu3 Sb, Cu4 Sn), and ␤-SnSb. The Gibbs energies of pure elements with respect to

Table 3 Invariant reactions in the ternary Sn–Sb–Cu system.

A B C D E F G

Type

Reaction

T experiment (◦ C)

T calculated (◦ C)

T [21] (◦ C)

Class II Class II Class II Class II Class II Class II Class I

L + Sn3 Sb2 = Sn + Cu6 Sn5 L + ␤-SnSb = Sn3 Sb2 + Cu6 Sn5 L + Cu2 Sb = Cu6 Sn5 + ␤-SnSb L + Sb = ␤-SnSb + Cu2 Sb L + Cu3 Sn = Cu6 Sn5 + Cu2 Sb L + (Cu3 Sb,Cu4 Sn) = Cu3 Sn + Cu2 Sb L = (Cu3 Sb,Cu4 Sn) + Cu + Cu17 Sn3

239 318 370 388 410 480 –

239 318 355 388 410 478 645

240 310 372 386 405 470 645

710

S.-w. Chen et al. / Materials Chemistry and Physics 132 (2012) 703–715

Table 4 Interaction parameters of the Sn–Sb–Cu system. Phase

Function

FCC A1(Cu)

298.15 < T < 1357.77: FCC A1 = −7770.458 + 130.485235 ∗ T − 24.112392 ∗ T ∗ LN(T ) − .00265684 ∗ T ∗ ∗2 + 1.29223E − 07 ∗ T ∗ ∗3 + 52478 ∗ T ∗ ∗(−1) GCu 1357.77 < T < 3200: FCC A1 = −13542.026 + 183.803828 ∗ T − 31.38 ∗ T ∗ LN(T ) + 3.64167E + 29 ∗ T ∗ ∗(−9) GCu 298.15 < T < 903.78: FCC A1 = GCu +10631.142 + 142.454689 ∗ T − 30.5130752 ∗ T ∗ LN(T ) + .007748768 ∗ T ∗ ∗2 − 3.003415E − 06 ∗ T ∗ ∗3 + 10,0625 ∗ T ∗ ∗(−1) 903.78 < T < 2000.00 Cu2 Sb = −4753.8475 − 3.3134858 ∗ T + .67 ∗ GHSERCU + .33 ∗ GHSERSB GCu:Sb 298.15 < T < 505.08 FCC GCu

A1

= −345.135 + 56.983315 ∗ T − 15.961 ∗ T ∗ LN(T ) − .0188702 ∗ T ∗ ∗2 + 3.121167E − 06 ∗ T ∗ ∗3 − 61960 ∗ T ∗ ∗(−1)

505.08 < T < 800.00 FCC A1 = GCu +8034.724 − 4.454731 ∗ T − 8.2590486 ∗ T ∗ LN(T ) − .016814429 ∗ T ∗ ∗2 + 2.623131E − 06 ∗ T ∗ ∗3 − 1, 081, 244 ∗ T ∗ ∗(−1) 800.00 < T < 3000.00 FCC A1 = −2746.959 + 130.53688 ∗ T − 28.4512 ∗ T ∗ LN(T ) − 1.2307E + 25 ∗ T ∗ ∗(−9) GCu

␤-Cu17 Sn3 -(BCC A2)

0 FCC A1 LCu,Sb

= −13550.628 − 6.3594596 ∗ T

0 FCC A1 LCu,Sb

= −10309.8452 + 1.15851139 ∗ T

1 FCC A1 LCu,Sn

= −16190.0328 + 6.49480816 ∗ T

0 FCC A1 LSn,Sb

= +50 ∗ T

298.15 < T < 1357.77: BCC A2 = −3753.458 + 129.230235 ∗ T − 24.112392 ∗ T ∗ LN(T ) − .00265684 ∗ T ∗ ∗2 + 1.29223E − 07 ∗ T ∗ ∗3 + 52478 ∗ T ∗ ∗(−1) GCu 1357.77 < T < 3200.00: BCC A2 = −9525.026 + 182.548828 ∗ T − 31.38 ∗ T ∗ LN(T ) + 3.64167E + 29 ∗ T ∗ ∗(−9) GCu 298.15 < T < 903.78: BCC A2 = GSb +10631.142 + 141.054689 ∗ T − 30.5130752 ∗ T ∗ LN(T ) + .007748768 ∗ T ∗ ∗2 − 3.003415E − 06 ∗ T ∗ ∗3 + 100625 ∗ T ∗ ∗(−1) 903.78 < T < 2000.00: BCC A2 = +8135.17 + 154.385872 ∗ T − 31.38 ∗ T ∗ LN(T ) + 1.616849E + 27 ∗ T ∗ ∗(−9) GSb 250.00 < T < 505.08: BCC A2 = −1455.135 + 59.443315 ∗ T − 15.961 ∗ T ∗ LN(T ) − .016814429 ∗ T ∗ ∗2 + 2.623131E − 06 ∗ T ∗ ∗3 − 1, 081, 244 ∗ T ∗ ∗(−1) GSn 505.08 < T < 800.00: BCC A2 GSn = +6924.724 − 1.994731 ∗ T − 8.2590486 ∗ T ∗ LN(T ) − .016814429 ∗ T ∗ ∗2 + 2.623131E − 06 ∗ T ∗ ∗3 − 1, 081, 244 ∗ T ∗ ∗(−1) 800.00 < T < 3000.00: BCC A2 = −3856.959 + 132.99688 ∗ T − 28.4512 ∗ T ∗ LN(T ) − 1.2307E + 25 ∗ T ∗ ∗(−9) GSn 0 BCC A2 LCu,Sn

= −41774.195 + 47.877361 ∗ T

1 BCC A2 LCu,Sn

= −12316.502 − 50.445819 ∗ T

0 BCC A2 LCu,Sb

= −30000.195 + 47.877361 ∗ T

1 BCC A2 LCu,Sb

= −12316.502 − 50.445819 ∗ T

012 BCC A2 LCu,Sb,Sn

Rhombohedral A7(Sb)

= −1000

298.15 < T < 903.78 : Rhombohedral A7 = GSb −9242.858 + 156.154689 ∗ T − 30.5130752 ∗ T ∗ LN(T ) + .007748768 ∗ T ∗ ∗2 − 3.003415E − 06 ∗ T ∗ ∗3 + 100, 625 ∗ T ∗ ∗(−l) 903.78 < T < 2000.00 : Rhombohedral A7 = −11738.83 + 169.485872 ∗ T − 31.38 ∗ T ∗ LN(T ) + 1.616849E + 27 ∗ T ∗ ∗(−9) GSb 250.00 < T < 505.08 : Rhombohedral A7 = −3820.135 + 65.443315 ∗ T − 15.961 ∗ T ∗ LN(T ) − .0188702 ∗ T ∗ ∗2 + 3.121167E − 06 ∗ T ∗ ∗3 − 61, 960 ∗ T ∗ ∗(−l) GSn 505.08 < T < 800.00 : Rhombohedral A7 = +4559.724 + 4.005269 ∗ T − 8.2590486 ∗ T ∗ LN(T ) − .016814429 ∗ T ∗ ∗2 + 2.623131E − 06 ∗ T ∗ ∗3 − 1, 081, 244 ∗ GSn T ∗ ∗(−l) − 1.2307E + 25 ∗ T ∗ ∗(−9)

800.00 < T < 3000.00 : Rhombohedral A7 = −6221.959 + 138.99688 ∗ T − 28.4512 ∗ T ∗ LN(T ) − 1.2307E + 25 ∗ T ∗ ∗(−9) GSn 0 Rhombohedral A7 LSn

= −2682.8508 + 8.0143951 ∗ T

S.-w. Chen et al. / Materials Chemistry and Physics 132 (2012) 703–715 Table 4 (Continued) Phase

Function 1 Rhombohedral A7 LSb,Sn

BCT A5(Sn)

BCT GCu

= −78.475078

= GHSERCU + 5000

A5

298.15 < T < 903.78 : BCT A5 = GSb +3757.42 + 148.154689 ∗ T − 30.5130752 ∗ T ∗ LN(T ) + .007748768 ∗ T ∗ ∗2 − 3.003415E − 06 ∗ T ∗ ∗3 + 100, 625 ∗ T ∗ ∗(−1) 903.78 < T < 2000.00 : BCT A5 = +1261.17 + 161.485872 ∗ T − 31.38 ∗ T ∗ LN(T ) + 1.616849E + 27 ∗ T ∗ ∗(−9) GSb 250.00 < T < 505.08 : BCT A5 = −5855.135 + 65.443315 ∗ T − 15.961 ∗ T ∗ LN(T ) − .0188702 ∗ T ∗ ∗2 + 3.121167E − 06 ∗ T ∗ ∗3 − 61, 960 ∗ T ∗ ∗(−l) GSn 505.08 < T < 800.00 : BCT GSn

= +2524.724 + 4.005269 ∗ T − 8.2590486 ∗ T ∗ LN(T ) − .016814429 ∗ T ∗ ∗2 + 2.623131E − 06 ∗ T ∗ ∗3 − 1081244 ∗ T ∗ ∗(−l)

A5

800.00 < T < 3000.00 : BCT A5 = −8256.959 + 138.99688 ∗ T − 28.4512 ∗ T ∗ LN(T ) − 1.2307E + 25 ∗ T ∗ ∗(−9) GSn 0 BCT A5 LSb,Sn

= −14643.227 + 6.637427 ∗ T

1 BCT A5 LSb,Sn

= −37586.893 + 62.244009 ∗ T

012 BCT A5 LCu,Sb,Sn

Liquid

= −30000

298.15 < T < 1357.77 : Liquid = +5194.277 + 120.973331 ∗ T − 24.112392 ∗ T ∗ LN(T ) − .00265684 ∗ T ∗ ∗2 + 1.29223E − 07 ∗ T ∗ ∗3 + 52, 478 ∗ T ∗ ∗(−l) − GCu 5.8489E − 21 ∗ T ∗ ∗7 1357.77 < T < 3200 : Liquid = −46.545 + 173.881484 ∗ T − 31.38 ∗ T ∗ LN(T ) GCu 298.15 < T < 903.78 : Liquid = +10579.47 + 134.231525 ∗ T − 30.5130752 ∗ T ∗ LN(T ) + .007748768 ∗ T ∗ ∗2 − 3.003415E − 06 ∗ T ∗ ∗3 + 100625 ∗ T ∗ GSb ∗(−l) − 1.74847E − 20 ∗ T 903.78 < T < 2000.00 : Liquid = +8175.359 + 147.455986 ∗ T − 31.38 ∗ T ∗ LN(T ) GSb 250 < T < 505.08 : Liquid

GSn = +1247.957 + 51.355548 ∗ T − 15.961 ∗ T ∗ LN(T ) − .0188702 ∗ T ∗ ∗2 + 3.121167E − 06 ∗ T ∗ ∗3 − 61, 960 ∗ T ∗ ∗(−1) + 1.47031E − 18 ∗ T ∗ ∗7 505.08 < T < 800.00 : Liquid = +9496.31 − 9.809114 ∗ T − 8.2590486 ∗ T ∗ LN(T ) − .016814429 ∗ T ∗ ∗2 + 2.623131E − 06 ∗ T ∗ ∗3 − 1081244 ∗ T ∗ ∗(−1) GSn 800.00 < T < 3000.00 Liquid

GSn

= −1285.372 + 125.182498 ∗ T − 28.4512 ∗ T ∗ LN(T )

0 Liquid LCu,Sn

= −15583.768 + 40.623909 ∗ T − 5.6172208 ∗ T ∗ LN(T )

1 Liquid LCu,Sn

= −27739.285 + 41.927049 ∗ T − 4.4641876 ∗ T ∗ LN(T )

2 Liquid LCu,Sn

= −13228.943 + .90582783 ∗ T

0 Liquid LCu,Sb

= −19797.1084 + 59.6783776 ∗ T − 8.74928734 ∗ T ∗ LN(T )

1 Liquid LCu,Sb

= −40331.126 + 78.2894974 ∗ T − 8.81488822 ∗ T ∗ LN(T )

Liquid GCu,Sb

= −29130.9086 + 13.3432514 ∗ T

3 Liquid LCu,Sb

= −5784.71138 + 6.41291099 ∗ T

4 Liquid LCu,Sb

= 9037.23823

0 Liquid LSb,Sn

= −5536.588 + 1.5399242 ∗ T

1 Liquid LSb,Sn

= 177.93161

2 Liquid LSb,Sn

= 883.18627

2

0 Liquid LCu,Sb,Sn

= + 131473.89 − 11.2335674 ∗ T

1 Liquid LCu,Sb,Sn

= −17228.6975 − 20.0146866 ∗ T

2 Liquid LCu,Sb,Sn

= −12204.1192 − 46.3210745 ∗ T

= −7080.1944 − .95535809 ∗ T + .769 ∗ GHSERCU + .231 ∗ GHSERSN

␨-Cu10 Sn3

Cu10 Sn3 GCu:Sn

␦-Cu41 Sn11

Cu41 Sn11 GCu:Sn = −6498.0861 − 1.0645957 ∗ T + .788 ∗ GHSERCU + .212 ∗ GHSERSN

711

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S.-w. Chen et al. / Materials Chemistry and Physics 132 (2012) 703–715

Table 4 (Continued) Phase

Function

Sn3 Sb2

Sb2 Sn3 GSb:Sn = −3295.8449 − .17391511 ∗ T + .43 ∗ GHSERSB + .57 ∗ GHSERSN Sb2 Sn3 = + 8729.4 − 17.647 ∗ T + .43 ∗ GHSERCU + .57 ∗ GHSERSN GSb:Cu

␥-Cu85 Sb15

Cu85 Sb15 GCu:Sb = −2845.6251 − 1.5505021 ∗ T + .85 ∗ GHSERCU + .15 ∗ GHSERSB

␧-Cu3 Sb

Cu75 Sb11 GCu:Sb = −5282.9886 − .82744487 ∗ T + .75 ∗ GHSERCU + .25 ∗ GHSERSB

␨-Cu77 Sb23

Cu77 Sb23 GCu:Sb = −5513.2492 − .051178622 ∗ T + .77 ∗ GHSERCU + .23 ∗ GHSERSB

␩-Cu2 Sb

Cu2 Sb GCu:Sb = −4753.8475 − 3.3134858 ∗ T + .67 ∗ GHSERCU + .33 ∗ GHSERSB Cu2 Sb = +100 + .67 ∗ GHSERCU + .33 ∗ GHSERSN GCu:Sn Cu2 Sb GCu:Sb,Sn = −5000

(Cu3 Sb,Cu4 Sn)-(GAMMA DO3)

␧-Cu3 Sn

GAMMA GCu:Cu

DO3

= GCUBCC

GAMMA DO3 GSb:Cu

= +105215.49 + 30.805659 ∗ T + .75 ∗ GHSERSB + .25 ∗ GHSERCU

GAMMA DO3 GSn:Cu

= +120979.1 + .75 ∗ GHSERSN + .25 ∗ GHSERCU

GAMMA GCu:Sb

= +1799.7612 − 10.649474 ∗ T + .75 ∗ GHSERCU + .25 ∗ GHSERSB

DO3

GAMMA DO3 GSb:Sb

= GSBBCC

GAMMA GSn:Sb

DO3

=0

GAMMA GCu:Sn

DO3

= −5917.6917 − 2.4386438 ∗ T + .75 ∗ GHSERCU + .25 ∗ GHSERSN

GAMMA DO3 GSb:Sn

=0

GAMMA GSn:Sn

= GSNBCC

DO3

0 GAMMA DO3 LCu:Cu,Sb

= +1866.2245 − 1.7628085 ∗ T

0 GAMMA DO3 LCu:Cu,Sn

= −2689.6334 − 1.7880585 ∗ T

1 GAMMA DO3 LCu:Cu,Sn

= +20004 − 3.7847763 ∗ T

0 GAMMA DO3 LCu,Sb:Sb

= +21425.483 − 24.000505 ∗ T

0 GAMMA DO3 LCu,Sn:Sn

= +46784.267 − 42.2191 ∗ T

Cu3 Sn GCu:Cu = +5534.4546 − .24167126 ∗ T Cu3 Sn GSn::Cu

+ GHSERCU

= +15470.377 + 7.7319282 ∗ T + .75 ∗ GHSERSN + .25 ∗ GHSERCU

Cu3 Sn = −4500 + .75 ∗ GHSERCU + .25 ∗ GHSERSB GCu:Sb Cu3 Sn =0 GSn::Sb Cu3 Sn = −8406.7389 + .10009523 ∗ T + .75 ∗ GHSERCU + .25 ∗ GHSERSN GCu:Sn Cu3 Sn = +14564.708 + .10013008 ∗ T GSn:Sn

Cu6 Sn5

+ GHSERSN

0 Cu3 Sn LCu,Sn::∗

= +.095536963 + . 10006002 ∗ T

0 Cu3 Sn L∗:Cu:Sn

= +217.49477 − 1.8316228 ∗ T

Cu6 Sn5 GCu:Cu = +10041.2953 − .35693806 ∗ T

+ GHSERCU

Cu6 Sn5 GSn:Cu =0 Cu6 Sn5 = +150 + .565 ∗ GHSERCU + .435 ∗ GHSERSB GCu:Sb Cu6 Sn5 = −8727.31556 + 2.34511023 ∗ T + .565 ∗ GHSERCU + .435 ∗ GHSERSN GCu:Sn Cu6 Sn5 GSn:Sb =0

␤-SnSb

0 Cu6 Sn5 LCu:Sn::∗

= −5765.03605 + 11.6892279 ∗ T

0 Cu6 Sn5 L∗:Cu:Sn

= −20569.2941 + 17.9486224 ∗ T

0 Cu6 Sn5 L∗:Cu:Sb

= −1000

0 Cu6 Sn5 L∗:Sb:Sn

= +10360 − 25.067 ∗ T

SbSn GCu:Cu =0 SbSn = +12346 − 19.78 ∗ T + .5 ∗ GHSERSB + .5 ∗ GHSERCU GSb:Cu SbSn GSn:Cu =0 SbSn =0 GCu:Sb SbSn = +GHSERSB + 3243.7917 GSb:Sb SbSn GCu:Sb =0

S.-w. Chen et al. / Materials Chemistry and Physics 132 (2012) 703–715

713

Table 4 (Continued) Phase

Function SbSn GSb:Sn = −2951.1569 − .52608471 ∗ T + .5 ∗ GHSERSN + .5 ∗ GHSERSB SbSn =0 GSn:Sb SbSn GSn:Sn = +4000 − .043093938 ∗ T + GHSERSN 0 SbSn LSb,Sn:Sb

=0

0 SbSn LSb,Sn:Sb

=0

0 SbSn LSn,Sn:Sb

= −573.04832

0 SbSn LCu,Sn:Sb

= −.573.04832 − 2 ∗ T

0 SbSn LSn,Sb:Sn

= −573.04832

CuSb DELTA GCu:Cu = +12000 + GHSERCU

␦-Cu4 Sb

CuSb DELTA GSb:Cu =0 CuSb DELTA = −5832.3378 + 1.1473054 ∗ T + .8 ∗ GHSERCU + .2 ∗ GHSERSB GCu:Sb CuSb DELTA GSb:Sb = +26677.996 + GHSERSB CuSb DELTA = +500 + .8 ∗ GHSERCU + .2 ∗ GHSERSN GCu:Sn CuSb DELTA GSb:Sn =0 0 CuSb DELTA L∗:Sb:Cu

= −8822.3743

0 CuSb DELTA LSb:Cu:∗

= −20839.024 − 2.7469306 ∗ T

0 CuSb DELTA L∗:Sb,Sn

= −10000

temperature 0 Gi (T ) = Gi (T ) − HiSER are represented by Eq. (1): 0

Gi (T )=a + bT + cT ln(T ) + dT 2 + eT −1 + fT 3 + iT 4 + jT 7 + kT −9 (1)

The 0 Gi (T ) data refer to the constant enthalpy value of the standard element reference HiSER at 298.15 K and 1 bar, as recommended by SGTE (Scientific Group Thermodata Europe) [34]. The reference states are: FCC A1 (Cu), BCT A5 (Sn), Rhombohedral A7(Sb). The 0 G (T ) expression may be given for several temperature ranges, i where the coefficients a, b, c, d, e, f, i, j, k have different values. The 0 Gi (T ) functions are taken from SGTE database [34]. 1. Substitutional solution: FCC A1(Cu), BCT A5(Sn), Rhombohedral A7(Sb), BCC A2(␤-Cu17 Sn3 ), and LIQUID. Solid and liquid solution phases are described by the substitutional solution model [35]: Gm (T ) =



xi 0 Gi (T ) + RT

i



xi ln(xi )

i



+

i

xi xj

  v

j>i





Lij (xi − xj )



v

(2)



v the xx part is the where i j>i i j v Lij (xi − xj ) Redlich–Kister polynomial for the excess Gibbs energy. 2. Stoichiometric compounds:␨-Cu10 Sn3 , ␦-Cu41 Sn11 , Sn3 Sb2 , ␥Cu17 Sb3 , ␨-Cu10 Sb3 , ␩-Cu2 Sb, and ␧-Cu3 Sb. Stoichiometric compounds are described as the line compound using the following [36]:

Gm (T ) = z + bT +



xi GJSERi

(3)

i

where GHSERi is a Gibbs energy of component i in a crystal structure stable at 298.15 K under pressure 1 bar. The functions in the Cu–Sn–Sb system are: GHSERCU = G of Cu in FCC A1

structure, GHSERSB = G of Sb in Rhombohedral A7 structure and GHSERSN = G of Sn in BCT A5 structure. 3. GAMMA DO3 (Cu3 Sb, Cu4 Sn) phase: the GAMMA DO3 phase is formed by an ordering process of the BCC A2(␤-Cu17 Sn3 ) phase. A description of the Gibbs free energy of this phase was proposed by Shim [37] as a two-sublattice model (Cu,Sn,Sb)0.75 (Sn,Cu,Sb)0.25 , and is represented by Eq. (4): 







I II 0 I II 0 I II 0 Gm (T ) = YCu ln YCu GCu:Cu + YCu ln YSn GCu:Sn + YSn ln YCu GSn:Cu 





I II 0 I II 0 I II 0 +YSn ln YSn GSn:Sn + YCu ln YSb GCu:Sb + YSb ln YCu GSb:Cu 

I II 0 I I +YSb ln YSb GSb:Sb + 0.75RT (0.435RT (YCu ln YCu I I I I II II +YSn ln YSn + YSb ln YSb ) + 0.25RT (YSn ln YSn 

II II II II +YSb ln YSb + YCu ln YCu ) + xs Gm

(4)

y

where xs Gm represents excess Gibbs energy, Yin denotes the site fraction of element i on sublattice N, symbol, “:” indicates separation of elements on the different sublattices, and “,” indicates separation of elements on the same sublattice. 4. ␧-Cu3 Sn phase: the ␧-Cu3 Sn phase in the Cu–Sn–Sb ternary system is characterized by a low solubility limit; however, experimental results show that this limit is not negligible [22]. More importantly, the␧-Cu3 Sn phase is frequently encountered in Cu–Sn-based systems, such as in the Sn–Ag–Cu, Sn–Cu–Ni and Sn–Ag–Cu–Ni systems [38–40], and its compositional homogeneities are usually significant in these systems. The ␧-Cu3 Sn phase is described by a two-sublattice compound energy formalism (Cu,Sn)0.75 :(Cu,Sn,Sb)0.25 : Cu3 Sn I II 0 Cu3 Sn I II 0 Cu3 Sn Gm (T ) = YCi ln YCi GCu:Cu + YCu ln YSn GCu:Sn I II 0 Cu3 Sn I II 0 Cu3 Sn I II 0 Cu3 Sn +YSn ln YCu GSn:Cu + YSn YSn GSn:Sn + YSn YSb GSn:Sb I II 0 Cu3 Sn I I I I +YCu YSb GCu:Sb + 0.75RT (YCu ln YCu + YSn ln YSn ) II II II II II II +0.25RT (YSn ln YSn + YCu ln YCu + YSb ln YSb ) Cu3 Sn +xs Gm

(5)

714

S.-w. Chen et al. / Materials Chemistry and Physics 132 (2012) 703–715

5. ␩-Cu6 Sn5 phase: the ␩-Cu6 Sn5 in this case was modeled by a two-sublattice model (Cu,Sn)0.565 :(Cu,Sb,Sn)0.435 . Antimony on the 2nd sublattice gives the necessary solubility of Sb in binary ␩Cu6 Sn5 phase. For this optimization, a simplified description of the ␩-Cu6 Sn5 phase is made. It is assumed that there is only one crystal structure of this phase, though in fact, there are two. Taking into account available experimental information, we were not able to reproduce the ␩-Cu6 Sn5 ↔ ␩ -Cu6 Sn5 transformation for a ternary system. Cu6 Sn5 I II 0 Cu6 Sn5 I II 0 Cu6 Sn5 I II 0 Cu6 Sn5 Gm (T ) = YCu YCu GCu:Cu + YCu YSn GCu:Sn + YCu YSb GCu:Sb I II 0 Cu6 Sn5 I I +YSn YSn GSn:Sn + 0.565RT (YCu ln YCu I I II II +YSn ln YSn ) + 0.435RT (YCu ln YCu II II II Cu6 Sn5 II +YSn ln YSn + YSb ln YSb ) + xs Gm

(6)

6. ␤-SnSb phase: this phase is modeled by a two-sublattice (Sb,Sn)0.5 :(Cu,Sb,Sn)0.5 compound energy model. The Gibbs free energy can be described by Eq. (7): SbSn I II 0 SbSn I II 0 SbSn I II 0 SbSn (T ) = YSb YSb GSb:Sb + YSb YSn GSb:Sn + YSn YSb GSn:Sb Gm I II 0 SbSn I II 0 SbSn I II 0 SbSn +YSn YSn GSn:Sb + YSn + YSn GSn:Sn + YSb YCu GSb:Sn I I I I +0.5RT (YSb ln YSb + YSn ln YSn ) II II II II II II +0.5RT (YSb ln YSb + YSn ln YSn + YCu ln YCu ) SbSn +xs Gm

(7)

It is noteworthy that there is previous discussion about the exact nature of the ␤-SnSb phase, its transformation and its structure at high temperatures [41]. However, there is not enough experimental information to propose proper thermodynamic descriptions of this transformation. Thus, the description of the ␤-SnSb phase in this study follows the proposition given by ASM Handbook [23]. 7. ␦-Cu4 Sb phase: the ␦-Cu4 Sbphase is a binary phase in the Cu–Sb system; however, it indicates significant solubility of Sn. In this case the phase was modeled using a two-sublattice Wagner–Shottky model (Cu,Sb)0.8 :(Cu,Sb,Sn)0.2 . Gibbs energy of this phase is described as follow: Delta I II 0 Delta I II 0 Delta I II Gm (T ) = YCu YCu GCu:Cu + YCu YSn GCu:Sn + YCu YSb I II +YSb YSb

0

0

Delta GCu:Sb

Fig. 8. (a) Calculated enthalpy of mixing of liquid phase at 1000 K superimposed with Lee et al. [14] data. Intersection 6 × x(Sn) − 4 × x(Cu) = 0. (b) Calculated enthalpy of mixing of liquid phase at 1000 K superimposed with Lee et al. [4] data. Intersection 7 × x(Sn) − 3 × x(Sb) = 0.

experimental data[14]. The activities of Sn obtained by Griffiths et al. [15] were measured in the Sn-rich corner, and the calculated results of this study are in good agreement with the experimental measurements as well. Since their samples [15] had neither a constant composition of one component nor a constant ratio of components, the comparison is not shown in figure. The calculated isothermal section superimposed with the nominal compositions of the samples is shown in Fig. 9, and experimental information agrees well with calculated phase equilibria.

Delta I I GSb:Sb + 0.8RT (YCu ln YCu

I I II II II II +YSb ln YSb ) + 0.2RT (YCu ln YCu + YSb ln YSb II II Delta +YSn ln YSn ) + xs Gm

(8)

5. Calculated results The binary phase diagram of Cu–Sb binary system has been originally described by using an associated solution liquid [18]. For extension into a ternary system, the description of the Cu–Sb binary liquid is changed from an associate solution to a substitutional solution, but the modeling of other phases remains the same [18]. The calculated Cu–Sb phase diagram is shown in Fig. 3(c) and the results reproduce the results by Gierlotka and Jendrzejczyk-Handzlik [18]. The thermodynamic parameters are listed in Table 4. Fig. 8(a) shows the calculated enthalpy of mixing of liquid phase at 726.85 ◦ C (1000 K) for the 6 × x(Sn) − 4 × x(Cu) = 0 intersection superimposed with the experimental determinations [14], and Fig. 8(b) shows those for the intersection 7 × x(Sn) − 3 × x(Sb) = 0. As shown in both Fig. 8(a) and (b), the calculated results are in good agreement with the

Fig. 9. Calculated isothermal section of Sn–Sb–Cu ternary system at 250 ◦ C.

S.-w. Chen et al. / Materials Chemistry and Physics 132 (2012) 703–715

However, the Sb solubilities in ␩-Cu6 Sn5 and ␧-Cu3 Sn phases determined by experiment are higher than those determined by calculation in this study. Since only two thermodynamic experimental data, the isothermal section at 250 ◦ C and the liquidus projection, are obtained in this study, there is not enough experimental information to fit the character of Sb solubility better. Fig. 6 shows the calculated liquidus projection superimposed with the experimental data. The calculated temperatures of invariant reactions agree well with those obtained by DTA experiment. Detailed information is given in Table 3. The shape of the liquidus projection and the primary solidification phases are similar to the results of Blalock et al. [21]. Most of the invariant temperatures determined in these two studies are close as well. The biggest differences can be found for the reactions, L + ␤-SnSb = Sn3 Sb2 + ␩Cu6 Sn5 for 8 degrees, and L + (␧-Cu3 Sb,Cu4 Sn) = ␧-Cu3 Sn + ␩-Cu2 Sb for 10 degrees. Detailed information about invariant reactions is given in Table 3. Moreover, Blalock et al. [21] published a figure entitled “Cu–Sb–Sn phases present at temperatures below the reactions in the solid state”. Unfortunately, this figure is not an isothermal section and could not be compared to our results. Based on reproductions of isothermal sections, liquidus projection, temperatures of invariant reactions and thermodynamic functions, it is concluded that the thermodynamic model describes the Sn–Sb–Cu ternary system well. 6. Conclusions The 250 ◦ C phase equilibria isothermal section and the liquidus projection of the Sn–Sb–Cu phase diagram were determined both experimentally and by calculation. No ternary phase is observed in this system. The Sn–Sb–Cu system has been modeled on the basis of experimental data and information from the literature. There are seven tie-triangles, L + Sn3 Sb2 + ␩-Cu6 Sn5 , Sn3 Sb2 + ␤-SnSb + ␩-Cu6 Sn5 , ␤-SnSb + ␧-Cu3 Sn + ␩-Cu6 Sn5 , ␤-SnSb + ␩-Cu2 Sb + ␧-Cu3 Sn, ␤-SnSb + Sb + ␩-Cu2 Sb, ␩-Cu2 Sb + ␦Cu4 Sb + ␧-Cu3 Sn and␦-Cu4 Sb + Cu + ␧-Cu3 Sn in Sn–Sb–Cu isothermal section at 250 ◦ C. Primary solidification phases in the Sn–Sb–Cu liquidus projection are ␧-Cu3 Sn, ␩-Cu6 Sn5 , Sn, Sn3 Sb2 , ␤-SnSb, Sb, ␩-Cu2 Sb, (␧-Cu3 Sb,Cu4 Sn), ␤-Cu17 Sn3 , and Cu. Seven invariant reactions in the Sn–Sb–Cu system were determined. Thermodynamic models of all the phases in the Sn–Sb–Cu ternary system are assessed. The calculated results are in good agreement with the experimental determinations. Acknowledgments The authors acknowledge financial support from the National Science Council of Taiwan (NSC95-2221-E-007-205). The authors also are grateful to the National Center for High-performance Computing for the use of PANDAT software and to Ms. Ru-Bo Chang for her help in preparing this document. References [1] J.W. Jang, P.G. Kim, K.N. Tu, M. Lee, High-temperature lead-free Sn–Sb solders: wetting reactions on Cu foils and phased-in Cu–Cr thin films, Journal of Materials Research 14 (10) (1999) 3895–3900. [2] S.W. Chen, P.Y. Chen, C.H. Wang, Melting point lowering of the Sn–Sb alloys caused by substrate dissolution, Journal of Electronic Materials 35 (11) (2006) 1982–1985. [3] S.G. Gonya, J.K. Lake, R.C. Long, R.N. Wild, Lead-free, tin, antimony, bismtuh, copper solder alloy, US patent 5,411,703, (1995). [4] S. Kusabiraki, M. Sumita, Solder alloy, US patent 6,229,248, (2001).

715

[5] W. Campbell, Lead–Tin–Antimony and Tin–Antimony–Copper alloys, Proceedings of the Annual meeting, American Society for Testing and Materials 13 (1913) 630–665. [6] W. Bonsack, The Sn–Cu–Sb system, Zeitschrift Metallkund 19 (1927) 107–110. [7] O.W. Ellis, G.B. Karelitz, A study of tin-base bearing metals, Transactions of the American Society of Mechanical Engineers 50 (1928) 13–28, MSP-50-11. [8] J.V. Harding, W.T. Pell-Walpole, The constitution of Sn-rich Sn–Sb–Cu alloys, Journal of the Institute of Metals 75 (1948) 15–130. [9] M. Tasaki, The ternary Cu–Sn–Sb system, Memoirs of the College of Science, Kyoto Imperial University, Series A, 12 (1929), 227–255. [10] C. Lee, C.Y. Lin, Y.W. Yen, The 260 ◦ C phase equilibria of the Sn–Sb–Cu ternary system and interfacial reactions at the Sn–Sb/Cu joints, Intermetallics 15 (2007) 1027–1037. [11] E. Gunzel, K. Schubert, Structural investigation in the Sb–Cu system, Zeitschrift Metallkunde 49 (1958) 124–133. [12] X.J. Liu, I. Ohnuma, C.P. Wang, M. Jiang, R. Kainuma, K. Ishida, M. Ode, T. Koyama, H. Onodera, T. Suzuki, Thermodynamic database on microsolders and copper-basedalloy systems, Journal of Electronic Materials 32 (11) (2003) 1265–1272. [13] L. Kaufman, H. Bernstin, Computer Calculation of Phase Diagrams: With Special References to Refractory Metals, Academic Press, New York, 1970. [14] J.J. Lee, B.J. Kim, W.S. Min, Calorimetric investigations of liquid Cu–Sb, Cu–Sn and Cu–Sb–Sn alloys, Journal of Alloys and Compounds 202 (1993) 237–242. [15] D.A. Griffiths, J. Braithwaite, L.W. Beckstead, G.R.B. Elliott, Journal of the Electrochemical Society 120 (2) (1973) 301–303. [16] W. Gierlotka, S.W. Chen, S.K. Lin, Thermodynamic description of the Cu–Sn system, Journal of Materials Research 22 (11) (2007) 3158–3165. [17] S.W. Chen, C.C. Chen, W. Gierlotka, A.R. Zi, P.Y. Chen, H.J. Wu, Phase equilibria of the Sn–Sb binary system, Journal of Electronic Materials 37 (7) (2008) 992–1002. [18] W. Gierlotka, D. Jendrzejczyk-Handzlik, Thermodynamic description of the Cu–Sb binary system, Journal of Alloys and Compounds 484 (2009) 172–176. [19] C.H. Lin, S.W. Chen, C.H. Wang, Phase equilibria and solidification properties of Sn–Cu–Ni alloys, Journal of Electronic Materials 31 (9) (2002) 907–915. [20] C.H. Wang, S.W. Chen, Isothermal section of the ternary Sn–Cu–Ni system and interfacial reactions in the Sn–Cu/Ni couples at 800 ◦ C, Metallurgical and Materials Transactions A 34A (2003) 2281–2287. [21] J.M. Blalock Jr., J.V. Harding, W.T. Pell-Walpole, Cu–Sb–Sn, in: T. Lyman, H.E. Boyer, W.J. Carnes, M.W. Chevalier, E.A. Durand, P.M. Unterweiser, H. Baker, P.D. Harvey, H.L. Waldorf, H.V. Bukovics, C.W. Kirkpatrick, J.W. Kothera (Eds.), Metals Handbook, 8, Metallography, Structures and Phase Diagrams, 8th ed., ASM, Metals Park, 1973, pp. 428–430. [22] N. Saunders, A.P. Miodownik, Bulletin of Alloy Phase Diagrams 11 (3) (1990) 278–287. [23] Hensen, Elliott, ASM Handbook, in: H. Baker (Ed.), Alloy Phase Diagrams, vol. 3, ASM International, Material Park, OH, 1992. [24] F.N. Rhines, Phase Diagrams in Metallurgy: Their Development and Application, McGraw-Hill, New York, 1956. [25] S.W. Chen, J.I. Lee, C.N. Chiu, Liquidus projection of the ternary As–Sn–Te system, Scripta Materialia 51 (9) (2004) 853–856. [26] S.W. Chen, C.C. Huang, J.C. Lin, The relationship between the peak shape of a DTA curve and the shape of a phase diagram, Chemical Engineering Science 50 (3) (1995) 417–431. [27] S.W. Chen, C.C. Lin, C.M. Chen, Determination of the melting and solidification characteristics of solders by using DSC, Metallurgical and Materials Transactions A 29A (1998) 1965–1972. [28] W.J. Boetinger, U.R. Kattner, K.-W. Moon, J.H. Perepezko, DTA and Heat Flux DSC Measurements of Alloy Melting and Freezing, NIST, Washington, 2006. [29] S.-L. Chen, Y. Yang, S.-W. Chen, X.-G. Lu, Y.A. Chang, Solidification simulation using Scheil Model in multicomponent systems, Journal of Phase Equilibria and Diffusion 30 (2009) 429–434. [30] N. Saunders, A.P. Miodownik, CALPHAD: Calculation of Phase Diagrams, A Comprehensive Guide, Pergamon, New York, 1998. [31] B. Sundman, B. Jansson, J.-O. Anderson, CALPHAD 9 (2) (1985) 153–190. [32] S.-L. Chen, K.C. Chou, Y.A. Chang, CALPHAD 17 (3) (1993) 287–302. [33] R. Schmid-Fetzer, D. Andersson, P.Y. Chevalier, L. Eleno, O. Fabrichnaya, U.R. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, M. Zinkevich, CALPHAD 31 (2007) 38–52. [34] A. Dinsdale:, SGTE data for pure elements, CALPHAD 15 (1991) 317–425. [35] E.A. Guggenheim, Mixtures, Clarendon Press, Oxford, London, 1952. [36] H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics, Cambridge University Press, Cambridge, 2007. [37] J.H. Shim, C.S. Oh, B.J. Lee, D.N. Lee, Zeitschrift Metallkunde 87 (1996) 205–212. [38] Y. Takatu, X. Liu, I. Ohnuma, R. Kainuma, K. Ishida, Materials Transactions 45 (3) (2004) 646. [39] J.W. Morris, J.L.F. Goldstein, Z. Mei, JOM 45 (7) (1993) 25–27. [40] W. Koster, T. Godecke, D. Heine, Zeitschrift Metallkunde 63 (1972) 820–825. [41] V. Vassiliev, M. Lelaurian, J. Hertz, A new proposal of the binary (Sn,Sb) phase diagram and its thermodynamic properties based on a new e.m.f. study, Journal of Alloys and Compounds 247 (1997) 223–233.