Experimental investigation and thermodynamic calculations of the Ag–Ga–Sn phase diagram

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

Contents lists available at ScienceDirect

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad

Experimental investigation and thermodynamic calculations of the Ag–Ga– Sn phase diagram

MARK

⁎

Milena Premovića,b, , Yong Dub, Dusko Minića, Bo Sundmanb,c, Cong Zhangb, Andy Watsond, Dragan Manasijeviće, Aleksandar Djordjevića a

University of Priština, Faculty of Technical Science, Kos. Mitrovica, Serbia State Key Laboratory of Powder Metallurgy, Central South University, Changsha, PR China c CIRIMAT, UPS/CNRS/ENSIACET, 116 Route de Narbonne, 31077 Toulouse, France d University of Leeds, Leeds, UK e University of Belgrade, Technical Faculty, Bor, Serbia b

A R T I C L E I N F O

A BS T RAC T

Keywords: Ternary Ag–Ga–Sn system Thermodynamic assessment CALPHAD

Phase equilibria in the Ag–Ga–Sn ternary system have been studied experimentally by using differential thermal analysis (DTA), scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD). Three vertical sections (Ag–Ga50Sn50, Ga–Ag50Sn50 and Sn–Ag50Ga50) and one isothermal section at 100 °C were experimentally established. Based on available information in the literature and present experimental results, a thermodynamic description of the ternary Ag-Ga-Sn system has been developed by using CALPHAD method. Reasonable agreement between experimental data and the calculated phase diagrams is reached. The liquid projection and invariant equilibria have been calculated by using presently obtained thermodynamic parameters.

1. Introduction Due to existing environmental policies and green trends in industry lead-free solders are attracting considerable attention over the last decade. Considering the wide application of these important materials, it is not entirely unexpected that a larger number of studies on this subject can be found in literature [1–8]. The potential substitutes for lead in lead-free solders need to fulfill many requirements in terms of mechanical and electrical properties as well as corrosion resistance. Lead and silver both have fcc crystal structure and similar properties such as density, malleability, ductility and workability. In addition, silver has very high electrical and thermal conductivity and possesses very low contact resistance. Consequently, silver based alloys represent a very good substitution for harmful lead-based solders and are commonly used in soldering in many industrial areas. Although ternary Ag-Ga-Sn system may not be considered as a commercially viable, it has interesting features in its own right and its complete description complements COST program. To date, only few studies on phase diagram on this system could be found in literature [9–12]. Thus descriptions of three vertical sections Ag–Ga50Sn50, Ga–Ag50Sn50, Sn–Ag50Ga50 and isothermal section at 100 °C were measured in this work. Temperatures phase transitions

⁎

were investigated using Differential Thermal Analysis (DTA). Microstructures of the selected samples at 100 °C were analyzed by scanning electron microscopy and energy dispersive X-ray spectrometry. Experimentally determined results and literature data [10] were used for thermodynamic modeling of the ternary system. Thermodynamic data for three sub-binary systems are taken from the literature. Thermodynamic parameters for the Ag–Ga binary system were taken from Gierlotka and Jendrzejczyk-Handzlik [13], for the binary Ag–Sn system from Gierlotka [14], Liu et al. [15], Luef et al. [16] and Liu et al. [17] and for binary Ga–Sn system from Anderson and Ansara [18]. Gibbs energies for pure elements are from recent SGTE compilation [19]. 2. Literature data 2.1. Binary systems Inconsistent descriptions of the Ag–Ga binary system can be found in literature and the main difference is about the existence of Ag3Ga2 intermetallic compound. Feschotte and Bass [20] have described this phase as AgGa. This was adopted by Okamoto [21] in his assessment of the Ag–Ga binary system. On the other hand, on the basis of literature

Corresponding author at: University of Priština, Faculty of Technical Science, Kos. Mitrovica, Serbia. E-mail address: [email protected] (M. Premović).

http://dx.doi.org/10.1016/j.calphad.2017.01.010 Received 17 December 2016; Received in revised form 27 January 2017; Accepted 29 January 2017 Available online 04 February 2017 0364-5916/ © 2017 Elsevier Ltd. All rights reserved.

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

M. Premović et al.

evaluation Zhang et al. [22] have reported the existence of Ag3Ga2 instead of AgGa, and also carried out the thermodynamic optimization of the Ag–Ga system. A number of different studies [23] related to this binary system can be found. Recent re-optimization of Ag-Ga system was carried out by Gierlotka and Jendrzejczyk-Handzlik [13] considering a large number of data. A good agreement between experimental [24–26] and calculated data has been obtained [13]. Fig. 1 present the calculated Ag-Ga phase diagram based on parameter given by Gierlotka and Jendrzejczyk-Handzlik [13]. The calculated Ag-Sn phase diagram, as shown in Fig. 2, is according to Gierlotka [14], Liu et al. [15], Luef et al. [16] and Liu et al. [17]. A large number of researchers have investigated this system [27–30]. The Ag-Sn binary system consists of four solid phases. Enthalpies of mixing for liquid phase were determined by calorimetric measurements [31–33] and recently by Flandorfer et al. [34] at seven different temperatures, whereas the chemical potential of Ag in the liquid phase were measured using electromotive force method (emf) [35–40]. The Ga-Sn phase diagram is a simple eutectic system with the eutectic at 20.9 °C. Three solid phases can be observed. Anderson and Ansara [18] reported the thermodynamic parameters for the Ga-Sn binary system, which were based on experimental studies of a large number of authors [41,42]. The calculated and experimental data were found to be in a good agreement. Thermodynamic activities of Ga and of Sn in liquid Ga–Sn alloys have been measured by Katayama et al. [43]. Zivkovic et al. [44] measured the mixing enthalpy of Ga–Sn liquid alloys in the 350–650 K temperature range. Calculated Ga–Sn phase diagram is shown in Fig. 3. The crystal structure data for the solid phases in the constitutive binary systems are listed in Table 1.

Fig. 1. Calculated Ag–Ga phase diagram [13].

2.2. Ag–Ga–Sn ternary system Prince [9] has presented a summary of the phase diagram data for Ag-Ga-Sn system. The ternary alloy GaSn3.5Ag3 wt% has been studied by Song et al. [11] using DSC. Weibke and Hesse [12] investigated the isothermal section at 0 °C and two vertical sections, one with constant amount of Ag (30 at%) and the other with 30 at% Sn, by means of metallographic, thermal and x-ray technique. Based on experimental results of the isothermal section at 0 °C, ε-Ag3Sn phase from Ag-Sn forms with δ phase from Ag-Ga (δ phase 50 at% Ga forms by eutectic reaction at 326 °C) series of solid solution (Ag6Ga9xSn2-2X) [12]. Later investigations of the binary Ag-Ga system did not confirm the existence of δ. Amended vertical sections Ag30-GaSn and other Sn30-AgGa [12] are based on solid solution Ag6Ga9XSn2-2X. Li et al. [10] have been measurement partial and integral enthalpies of mixing of Ag–Ga–Sn alloys at 803 K along the seven sections.

Fig. 2. Calculated Ag–Sn phase diagram [14–17].

3. Experimental procedure All samples were prepared from Ag, Ga and Sn shots with 99.999 at % purity in an induction furnace under high purity argon atmosphere. The average weight loss of the samples during melting was about 1 mass %. Prepared samples for the SEM–EDS investigation were placed in quartz tube, sealed under vacuum and equilibrated at 100 °C for three weeks and quenched into water and ice mixture in order to preserve the equilibrium compositions at designated temperature. The average weight loss of the samples during annealing was less than 0.5 mass %. The equilibrium compositions of phases were determined by JEOL JSM-6460 scanning electron microscope with energy dispersive X-ray spectrometry, EDS (Oxford Instruments). Powder XRD data for phase identification of samples were recorded on a D2 PHASER (Bruker) powder diffractometer equipped with a dynamic scintillation detector and ceramic X-ray Cu tube (KFL-Cu-2K) in a 2θ range from 5° to 75° with a step size of 0.02°. The patterns were

Fig. 3. Calculated Ga–Sn phase diagram [18].

216

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

M. Premović et al.

Table 1 Crystal structure data for the solid phases in the Ag-Ga-Sn system. Thermodynamic database name

Phase

Pearson symbol/prototype

Space group

Lattice parameters (Å)/reference a

FCC_A1 ORTHO_A11 HCP_A3 HCP_ORD

(Ag) (Ga) ζ-Ag2Ga ζ′-Ag2Ga

cF4/Cu oS8/Orth-Ga hP2/Mg hP9/Mg2In

AG3GA2 BCT_A5 DIAMOND_A4 HCP_A3 AG3SN

Ag3Ga2 (βSn) (αSn) ζ-Ag4Sn ε-Ag3Sn

… tI4/beta Sn cF8/C hP2/Mg oP8/Cu3Ti

Fm 3m Cmca P63/mmc P 62 m Pmmm I41/amd Fd 3m P63/mmc Pmmn

Table 2 Phase transition temperatures along three vertical sections in the Ag-Ga-Sn system. Nominal composition (at%)

Vertical section Ag–Ga50Sn50 Ag10Ga45Sn45 Ag20Ga40Sn40 Ag30Ga35Sn35 Ag40Ga30Sn30 Ag60Ga20Sn20 Ag80Ga10Sn10 Ag90Ga5Sn5

25.3 27.9 26.1 26.3 108.3 147.4 74.5

143.2 148.1 168.2 190.1 188.4 547.4 784.3

Vertical section Ga–Ag50Sn50 Ag40Ga20Sn40 Ag30Ga40Sn30 Ag25Ga50Sn25 Ag20Ga60Sn20 Ag10Ga80Sn10 Ag5Ga90Sn5

106.3 26.7 25.2 25.3 27.1 27.4

188.5 147.9 111.8 98.3 48.9

Vertical section Sn–Ag50Ga50 Ag40Ga40Sn20 Ag30Ga30Sn40 Ag25Ga25Sn50 Ag20Ga20Sn60 Ag10Ga10Sn80

26.1 27.3 28.1 25.9 173.3

148.6 179.4 192.4 191.4 190.8

405.2 440.5 455.9 479.8 579.6 752.1 862.5

656.4

223.8 230.1 250.6 227.3

225.4 201.3 203.2 204.1

243.1 250.9

250.6 223.8

7.6602 [46]

4.5258 [46] 4.6956 [23] 2.8788 [23]

3.8764 [47]

3.1802 [47] 3.1819 [48]

4.7802 [51]

4.7842 [50] 5.1843 [51]

Alloy composition (at%)

Experimental observed phases

Compositions of phases (at%) Ag

Ga

Sn

1.

55.21 Ag 14.88 Ga 29.91 Sn

ε ζ′ (βSn)

74.72 ± 0.18 67.20 ± 0.1 0.27 ± 0.05

0.42 ± 0.02 32.60 ± 0.11 0.97 ± 0.16

24.86 ± 0.07 0.20 ± 0.21 98.76 ± 0.42

2.

30.55 Ag 24.05 Ga 45.40 Sn

Ag3Ga2 (βSn)

58.71 ± 0.11 0.16 ± 0.07

40.51 ± 0.16 7.74 ± 0.15

0.78 ± 0.09 92.10 ± 0.13

3.

45.32 Ag 24.67 Ga 30.01 Sn

Ag3Ga2 ζ′ (βSn)

58.86 ± 0.08 66.87 ± 0.15 0.26 ± 0.13

40.81 ± 0.08 32.75 ± 0.07 0.43 ± 0.12

0.33 ± 0.18 0.38 ± 0.16 99.31 ± 0.20

4.

30.28 Ag 20.63 Ga 49.09 Sn

Ag3Ga2 (βSn)

59.57 ± 0.12 0.23 ± 0.21

39.85 ± 0.23 1.35 ± 0.15

0.58 ± 0.15 98.42 ± 0.18

5.

35.37 Ag 34.92 Ga 29.71 Sn

L Ag3Ga2 (βSn)

1.17 ± 0.13 59.16 ± 0.15 0.26 ± 0.12

67.81 ± 0.14 40.01 ± 0.13 8.21 ± 0.08

31.02 ± 0.07 0.83 ± 0.02 91.53 ± 0.23

6.

30.39 Ag 33.21 Ga 36.40 Sn

L Ag3Ga2 (βSn)

0.84 ± 0.17 59.46 ± 0.24 0.77 ± 0.18

67.81 ± 0.05 39.81 ± 0.15 7.31 ± 0.13

31.35 ± 0.13 0.73 ± 0.18 91.92 ± 0.19

No

Liquid

236.9 227.7 218.0 221.4

6.7271 [47] 5.8318 [48] 6.4892 [49] 2.9658 [50] 5.968 [51]

c

Table 3 Experimentally determined phase composition in the ternary Ag–Ga–Sn system at 100 °C.

Phase transition temperatures (°C) Other peak

4.08626 [45] 4.5198 [46] 2.8818 [23] 7.7710 [23]

b

480.9 449.1 437.5 409.1 320.1 250.1

475.8 450.2 447.9 437.9 357.9

analyzed using the Topas 4.2 software, ICDD databases PDF2 (2013). The phase transformation temperatures were determined by DTA method using SDT Q600 (TA instruments). Alumina crucibles were used and measurements were performed under flowing nitrogen atmosphere. Sample mass and heating rate were determined by analysis of one sample under different testing conditions. The sample was analyzed under heating rates of 5, 10 and 15 °C/min. It was found that the DTA curve obtained at the heating rate of 5 °C/min has slightly more pronounced peaks than the other two. Different masses of the same sample were then analyzed at the heating of 5 °C/min and the sample mass in range 10–15 mg produced the most pronounced peaks. These sample mass and heating rates were adopted for analysis of all other samples.

nominal compositions along three vertical sections Ag–Ga50Sn50, Ga– Ag50Sn50 and Sn–Ag50Ga50 have been experimentally investigated using DTA. The invariant reaction temperatures were determined from the onset of the corresponding peak. The liquid temperatures were evaluated from the peak maximum. Obtained DTA data are given in Table 2 with a temperature accuracy of ± 1 °C. 4.2. Isothermal section at 100 °C Six ternary alloys from the isothermal sections at 100 °C were examined with SEM-EDS and XRD analysis. Six samples prepared in this work have the same compositions as those investigated by Weibke and Hesse [12]. Purpose of prepared samples is to observe the formation of ternary solid solution Ag6Ga9XSn2-2X. Three alloys 2, 4 and 6 are with constant amount of Ag 30 at% and three alloys 1, 3 and 5 with constant amount of Sn 30 at%. Alloy composition and the composition of the individual coexisting phases are given in Table 3. From samples 1–6, the existence of Ag6Ga9XSn2-2X has not

4. Experimental results 4.1. Vertical sections Phase transition temperatures of the 18 selected samples with

217

M. Premović et al.

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

Fig. 4. SEM micrographs of the six selected alloy samples annealed at 100 °C for three weeks.

confirmed. Based on microstructure of selected alloy 1 three phases ε(Ag3Sn), ζ′-(Ag2Ga) and (βSn) are found. Solubility of third element in intermetallic compound ε and ζ′ is negligible. Micrograph of sample 1 is given in Fig. 4a. A two-phase equilibrium of Ag3Ga2 and (βSn) was observed in samples 2 and 4. Fig. 4b and d present a microstructure of alloys 2 and 4, respectively. In both microstructures solid solution (βSn) is detected as a light phase with a measured solubility of Ga of 7.74 at% for sample 2 and of 1.35 at% for sample 4. Intermetallic compound Ag3Ga2 is detected as a gray phase in observed micro-

structures of samples 2 and 4. Three phases Ag3Ga2, ζ′ and (βSn) were detected in sample 3. Solubility of Sn in intermetallic compound Ag3Ga2 and ζ′ is very small. The Ag3Ga2 phase is detected as a dark phase at the end of a ζ′ phase grain. Detected solubility of Ga in solid solution (βSn) is low. Three-phase equilibrium of L, Ag3Ga2 and (βSn) was detected in samples 5 and 6. Micrographs of samples are given on Fig. 4e and f. Liquid phase L with composition Ag1.17Ga67.81Sn31.02 at% (sample 5) and Ag0.84Ga67.81Sn31.35 at% (sample 6) is trapped between grain of Ag3Ga2 and (βSn) phase. Solid solution (βSn) is light phase

218

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

M. Premović et al.

The ternary liquid phase is treated as substitutional solution. The Gibbs free energy is expressed by the Redlich-Kister-Muggianu polynomial [55]:

Table 4 XRD analysis of six Ag-Ga-Sn alloy samples annealed at 100 °C for three weeks. No

Determined phases

Lattice parameters (Å)

XRD

a Exp.

b Exp.

c Exp.

ε ζ′ (βSn)

5.96088(3) 7.75927(4) 5.83571(2)

4.79651(5)

5.17716(5) 2.87626(2) 3.18127(8)

2

Ag3Ga2 (βSn)

6.72987(1) 5.82903(1)

3.87538(1)

3.18674(4) 3.16208(3)

3

Ag3Ga2 ζ′ (βSn)

6.72654(7) 7.76541(1) 5.83501(3)

3.87921(2)

3.18798(2) 2.87938(6) 3.18279(2)

4

Ag3Ga2 (βSn)

6.72765(4) 5.83906(9)

3.87675(5)

3.18987(7) 3.18756(5)

5

L Ag3Ga2 (βSn)

– 6.72656(1) 5.83897(1)

– 3.87879(2)

– 3.18657(2) 3.16009(3)

L Ag3Ga2 (βSn)

– 6.72657(5) 5.81787(1)

– 3.87931(3)

1

6

L L L + xGa GGa + xSn GSn + RT (xAg ln xAg + xGa ln xGa + xSn ln xSn ) GmL = xAg GAg L + xAg xGa LAg , Ga ex L L L + xAg xSn LAg , Sn + xGa xSn LGa, Sn + GAg, Ga, Sn

(1) where xAg , xGa and xSn are molar fractions of elements Ag, Ga and Sn, L L L , GGa and GSn are the Gibbs energies of Ag, Ga and Sn in respectively GAg liquid phase. R is gas constant, T temperature, and RT (xAg ln xAg + xGa ln xGa + xSn ln xSn ) corresponds to the contribution L L of the ideal entropy of mixing to the Gibbs energy. LAg , Ga , LAg, Sn and L LGa, Sn are interaction parameters from the corresponding binary systems from ref. [13–18]. Last term in Eq. (1) is the ternary excess Gibbs energy, which is expressed as: L 0 L 1 L 2 L GAg , Ga, Sn = xAg xGa xSn (xAg LAg, Ga, Sn + xGa LAg, Ga, Sn + xSn LAg, Ga, Sn )

ex

(2)

2 L L 1 L where 0LAg , Ga, Sn , LAg, Ga, Sn and LAg, Ga, Sn are ternary i L meters expressed as LAg, Ga, Sn = ai + bi T and ai , bi are

interaction paramodel parameters which need to be optimized from the experimental phases diagram and/or thermodynamic data.

– 3.17989(8) 3.16439(4)

6. Thermodynamic calculations Based on literature data of integral and partial enthalpy of formation of Ag-Ga-Sn ternary alloys at 803 K [10] and present experimental data, the thermodynamic optimization of Ag-Ga-Sn system has been performed. The optimization of the parameters for liquid was conducted using the PARROT module [56] based on a least square procedure. The step-by step optimization procedure described by Du et al. [57] was utilized in the present assessment. The optimization begins with literature data from Li et al. [10] and first temperature independent parameters are adjusted. In the second step a temperature dependent parameters for liquid phase are evaluated using present experimental data. Finally all thermodynamic parameters for liquid phase were optimized simultaneously by taking all the experimental data. The thermodynamic parameters for liquid phase obtained in this work are presented in Eq. (3a)–(3c) in the unit of J/mol of atom:

Fig. 5. XRD pattern for the sample 1.

with a detected solubility of Ga 8.21 at% (sample 5) and 7.31 at% (sample 6). Third phase is intermetallic compound Ag3Ga2 which is detected as a gray phase. Additionally six samples are investigated with XRD analysis and results are given in Table 4. XRD patterns of detected phases were compared with the literature data [23,47,48,51]. In Fig. 5 is given XRD pattern of alloy 1 with marked picks of detected phases.

0 L LAg, Ga, Sn

= 107468.819 − 100⋅T

(3a)

1 L LAg, Ga, Sn

= 28443.7702 + 29.24⋅T

(3b)

2 L LAg, Ga, Sn

= 4780.45309 + 29.86⋅T

(3c)

All of the binary compounds are treated as a pure binary ones since the solid solubility for the third element is negligible. In Fig. 6 are presented four of seven calculated integral enthalpies of mixing at 803 K along with the experimental values reported by Li et al. [10]. The calculations are in reasonable agreement with the experimental thermodynamic properties [10]. Difference from the AgGa rich side is related to different data for the description of binary Ag-Ga system used in this work and reference [10]. In Fig. 7 are presented calculated three vertical sections compared with experimental determined temperatures of phase transformation. As can be seen from the Fig. 7, the calculations are in agreement with most of the experimental data. The calculated isothermal section at 100 °C is shown in Fig. 8 compared with the present experimental data.

5. Thermodynamic modeling The Ag–Ga–Sn ternary system was thermodynamically assessed by CALPHAD method [52,53] using Thermo-calc software package [54]. Thermodynamic parameters for constitutive binary systems were taken from literature [13–18].

219

M. Premović et al.

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

Fig. 6. Calculated integral enthalpy of mixing at 803 K in comparison with the experimental data [10]: a) x(Ag)/x(Ga)=1/1, b) x(Ag)/x(Ga)=1/3, c) x(Ga)/x(Sn)=1/3 and d) x(Ga)/x(Sn) =3/1.

experimentally by DTA, SEM–EDS and XRD analysis and modeled by CALPHAD method. Investigated samples are from three vertical sections and isothermal section at 100 °C. Results of EDS analysis did not confirm the existence of solid solution Ag6Ga9XSn2-2X reported in literature [12]. Detected phases by EDS are confirmed by XRD analysis. Temperatures of phase transition along three vertical sections are experimentally determined. Based on the present experimental data and experimental data from literature [10] thermodynamic modeling of the Ag-Ga-Sn system was performed. Good agreement with calculated and experimental data is reached. Based on data for constituent binary systems and assessed ternary parameters for liquid phase the liquidus surface projection of the ternary Ag–Ga–Sn system was calculated. On the calculated liquidus surface projection four invariant reactions and seven primary crystallization fields can be observed.

As shown in Fig. 8, a good agreement between calculation and experiment is visible. Based on thermodynamic data for constituent binary systems from the literature and presented assessed ternary parameters for liquid, the liquidus surface projection of the ternary Ag–Ga–Sn system was calculated and presented in Fig. 9. As can be seen from Fig. 9 there are seven primary crystallization fields: (Ag), (Ga), (βSn), ζ, ζ′, Ag3Ga2 and ε. Furthermore, from the presented liquidus surface projection, the existence of four invariant reactions can be observed. The predicted invariant reactions are listed in Table 5 and in Fig. 10 is presented a reaction scheme for the system. Three out of four observed invariant reactions are U – type reactions and one is the E – type reaction. 7. Conclusions Phase diagram of the Ag–Ga–Sn ternary system was investigated

220

M. Premović et al.

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

Fig. 7. Calculated vertical sections of the Ag–Ga–Sn ternary system compared with the present experimental data: a) Ag-GaSn, b) Ga-AgSn and c) Sn-AgGa.

Fig. 9. Calculated liquidus projection of the ternary Ag–Ga–Sn system.

Fig. 8. Calculated isothermal section at 100 °C compared with the experimental data.

221

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

M. Premović et al.

Table 5 The invariant reactions in the Ag–Ga–Sn ternary system. Temperature (°C)

Invariant reaction

Type

at% (Ag)

at% (Ga)

at% (Sn)

303.4

L+ζ′-Ag2Ga- > Ag3Ga2+ζ-Ag2Ga L+ε-Ag3Sn- > (βSn)+ζ-Ag4Sn L+ζ- > Ag3Ga2+(βSn) L- > Ag3Ga2+(βSn)+(Ga)

U1

0.1125

0.8474

0.0401

U2

0.0383

0.0107

0.9510

U3

0.0134

0.1568

0.8298

E1

0.0002

0.9230

0.0768

217.6 191.7 20.6

Fig. 10. The reaction scheme for liquid phase of the Ag-Ga-Sn system according to presented calculations with temperature in °C. durch gallium, Z. Elektrochem. 46 (3) (1940) 219–222. [13] W. Gierlotka, D. Jendrzejczyk-Handzlik, Thermodynamic description of the binary Ag–Ga system, J. Alloy. Compd. 509 (2011) 38–42. [14] W. Gierlotka, Thermodynamic description of the quaternary Ag-Cu-In-Sn system, J. Electron. Mater. 41 (1) (2012) 86–108. [15] Z.J. Liu, Y. Inohara, Y. Takaku, I. Ohnuma, R. Kainuma, K. Ishida, Z. Moser, W. Gasior, J. Pstrus, Experimental determination and thermodynamic calculation of the phase equilibria and surface tension in the Sn-Ag-In system, J. Electron. Mater. 31 (2002) 1139–1151. [16] C. Luef, H. Flandorfer, H. Ipster, Lead-free solder materials: experimental enthalpies of mixing in the Ag–Cu–Sn and Cu–Ni–Sn ternary systems, Z. Metallkd. 93 (2004) 151–163. [17] X.J. Liu, H.S. Liu, I. Ohnuma, R. Kainuma, K. Ishida, S. Itabashi, K. Kameda, K. Yamaguchi, Experimental determination and thermodynamic calculation of the phase equilibria in the Cu-In-Sn system, J. Electron. Mater. 30 (9) (2001) 1093–1103. [18] T.J. Anderson, I. Ansara, An assessment of the phase diagram and thermochemistry of the Ga-Sn system, J. Phase Equilib. 13 (2) (1992) 181–189. [19] A.T. Dinsdale, SGTE pure element database ver. 4.4, Calphad 15 (1991) 317–425. [20] P. Feschotte, P. Bass, Un nouveau composé intermétallique très timide: AgGa, J. Less Common Met. 171 (1) (1991) 157–162. [21] H. Okamoto, Ag-Ga (silver-gallium), J. Phase Equilib. 13 (3) (1992) 324–325. [22 Y. Zhang, J.B. Li, J.K. Liang, Q.L. Liu, Y.G. Xiao, Q. Zhang, G.H. Rao, C.R. Li, Thermodynamic assessment of the Ag-Ga system, Calphad 30 (3) (2006) 316–322. [23] Y. Zhang, Q.L. Liu, J.B. Li, J.K. Liang, J. Luo, F.S. Liu, Y.G. Xiao, G.H. Rao, Structures of the ζ and ζ′ phases in the Ag–Ga system, J. Alloy. Compd. 399 (2005) 155–159. [24] A.E. Gunneas, O.B. Karlsen, A. Olsen, P.T. Zagierski, Phase relations and crystal structures in the Ag–Ga system, J. Alloy. Compd. 297 (1–2) (2000) 144–155. [25] E. Weibke, K. Meisel, L. Wiegles, Das zustandsdiagramm des systems silber– gallium, Z. Anorg. Allg. Chem. 226 (1936) 201–208. [26] B. Predel, D.W. Stein, Bildungsenthalpien binärer verbindungen des galliums mit kupfer, silber und gold sowie analyse der thermodynamischen eigenschaften von 32-elektronen-verbindungen, Acta Matеr. 20 (5) (1972) 681–692. [27] Y. Liu, J. Wang, Y. Du, G. Sheng, L. Zhang, D. Liang, Study of diffusion and atomic mobilities for fcc Ag–Cd and Ag–Sn solder alloys, Calphad 35 (2) (2011) 224–230. [28] H. Mavoori, J. Chin, S. Vaynman, B. Moran, B. Keep, M. Fine, Stress relaxation, and plastic deformation in Sn–Ag and Sn–Zn eutectic solders, J. Electron. Mater. 26 (1997) 783–790. [29] F. Vnuk, M.H. Ainsley, R.W. Smith, The solid solubility of silver, gold and zinc in metallic tin, J. Mater. Sci. 16 (1981) 1171–1176. [30] C.S. Oh, J.H. Shim, J.B. Lee, N.D. Lee, A thermodynamic study on the Ag-Sb-Sn system, J. Alloy. Compd. 238 (1996) 155–166. [31] O.J. Kleppa, A calorimetric investigation of the system silver-tin at 450 °C, Acta

Acknowledgements This work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, project No. OI172037 and 2011 Union-Innovative Center of Central South University of China. References [1] M. Kopyto, B. Onderka, L.A. Zabdyr, Thermodynamic properties of the liquid Ag– Cu–Sn lead-free solder alloys, Mater. Chem. Phys. 122 (2–3) (2010) 480–484. [2] I. Dervišević, D. Minić, N. Talijan, M. Ristić, Experimental investigation and thermodynamic prediction of the Au–Cu–Sb phase diagram, Mater. Chem. Phys. 129 (1–2) (2011) 451–456. [3] L. Liu, W. Zhou, B. Li, P. Wu, Interfacial reactions between Sn–8Zn–3Bi–xNi leadfree solders and Cu substrate during isothermal aging, Mater. Chem. Phys. 123 (2– 3) (2010) 629–633. [4] V. Gandova, K. Lilova, H. Malakova, B. Huber, N. Milcheva, H. Ipser, J. Vrestal, G. Vassilev, On the synthesis of Bi–based precursors for lead-free solders development, J. Min. Metall. Sect. B Metall. 46 ((1)B) (2010) 11–23. [5] D. Soares, C. Vilarinho, J. Barbosa, F. Samuel, L. Trigo, P. Bré, Effect of trace elements on the interface reactions between two lead-free solders and copper or nickel substrates, J. Min. Metall. Sect. B Metall. 43 ((2)B) (2007) 131–139. [6] T.B. Luo, Z. Chen, A.M. Hu, M. Li, Study on melt properties, microstructure, tensile properties of low Ag content Sn–Ag–Zn Lead-free solders, Mater. Sci. Eng. A 556 (30) (2012) 885–890. [7] J. Sopousek, J. Vřešťál, A. Zemanova, J. Bursi, Phase diagram prediction and particle characterisation of Sn-Ag nano alloy for low melting point lead-free solders, J. Min. Metall. Sect. B Metall. 48 ((3)B) (2012) 419–425. [8] A. Kroupa, A.T. Dinsdale, A. Watson, J. Vřešťál, A. Zemanova, P. Broz, The thermodynamic database COST MP0602 for materials for high-temperature leadfree soldering, J. Min. Metall. Sect. B Metall. 48 (3) (2012) 339–346. [9] A. Prince, G. Petzow, G. Effenberg (Eds.), A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams 2, VCH Publishers, New York, 1988, pp. 154–157. [10] D. Li, S. Delsante, W. Gong, G. Borzone, Partial and integral enthalpies of mixing of Ag–Ga–Sn liquid alloys, Thermochim. Acta 523 (2011) 51–62. [11] J.M. Song, Z.M. Wu, D.A. Huang, H.Y. Chuang, The effect of low-temperature solute elements on nonequilibrium eutectic solidification of Sn–Ag eutectic solders, J. Electron. Mater. 36 (12) (2007) 1608–1614. [12] F. Weibke, E. Hesse, Zur frage der ersetzbarkeit des quecksilbers in zahnplomben

222

M. Premović et al.

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 56 (2017) 215–223

Metall. 3 (1955) 255–259. [32] G.H. Laurie, A.W.H. Morris, J.N. Pratt, Electromotive-force and calorimetric studies of thermodynamic properties of solid and liquid silver-tin alloys, Trans. AIME 236 (1966) 1390–1395. [33] R. Rakotomavo, M. Guane-Escard, J.P. Bros, P. Guane, Enthalpies of formation at 1373 K of the liquid alloys Ag+ Au, Ag+ Sn, Au+ Sn and Ag+ Au+ Sn, Ber. BunsenGes. Phys. Chem. 88 (1984) 663–670. [34] H. Flandorfer, C. Luef, U. Saeed, On the temperature dependence of the enthalpies of mixing in liquid binary (Ag, Cu, Ni)–Sn alloys, J. Non-Cryst. Solids 354 (2008) 2953–2972. [35] G.R.B. Elliot, J.F. Lemons, Activities of molten tin alloys from EMF measurements, J. Electron. Soc. 114 (1967) 935–937. [36] P.J.R. Chowdhury, A. Gosh, Thermodynamic measurements in liquid Sn−Ag alloys, Metall. Trans. 2 (1971) 2171–2174. [37] P. Kubaschewski, C.B. Alcock, Thermodynamic properties of Ag+Sn alloys, J. Chem. Thermodyn. 4 (2) (1972) 259–266. [38] M. Iwase, M. Yasuda, S. Miki, T. Mori, A thermodynamic study of liquid tin-silver alloys by means of solid-oxide galvanic cell, Trans. JIM 19 (11) (1978) 654–660. [39] K. Kameda, Thermodynamic properties of liquid silver-tin alloys, Trans. JIM 28 (7) (1987) 542–549. [40] R. Farhi, G. Petot-Ervas, C. Petot, J.P. Auffredic, Etude thermodynamique des alliages liquides argent-etain, Fr. Phys. Chem. Liq. 4 (2–3) (1974) 171–182. [41] S. Delcroix, A. Defrain, J. Epelboin, Alloy diagrams of Ga (I) or (II) with Sn, Zn, or In, J. Phys. Radium 24 (1963) 17–20. [42] B. Predel, Constitution diagram and properties of Ga–Sn alloys, J. Less-Common Met. 7 (1964) 347–355. [43] I. Katayama, K. Maki, M. Nakano, T. Iida, Thermodynamic activity in liquid Ga–Sn alloys studied by EMF method, Mater. Trans. JIM 37 (5) (1996) 988–990. [44] D. Zivkovic, D. Manasijevic, Z. Zivkovic, Lj Balanovic, Calorimetric investigation of liquid Ga–Me (Me=Sn, Zn) alloys using Oelsen method, Metalurgija 43 (2) (2004) 71–75. [45] M.E. Straumanis, Neubestimmung der Gitterparameter, Dichten und thermischen

[46] [47]

[48] [49] [50] [51] [52]

[53] [54] [55]

[56]

[57]

223

ausdehnungskoeffizienten von silber und gold, und vollkommenheit der struktur, Monatsh. Chem. 102 (1971) 1377–1386. A.J. Bradley, The crystal structure of gallium, Z. Kristallogr. Krist. 91 (1935) 302–316. D. Minic, M. Premovic, D. Manasijevic, V. Cosovic, D. Zivkovic, A. Markovic, Experimental investigation and thermodynamic calculations of the Ag-Bi-Ga phase diagram, J. Alloy. Compd. 646 (2015) 461–471. V.T. Deshpande, D.B. Sirdeshmukh, Thermal expansion of tetragonal tin, Acta Crystallogr. 14 (1961) 355–356. J. Thewlis, A.R. Davy, Thermal expansion of grey tin, Nature 174 (1954) (10111011). H.W. King, T.B. Massalski, Lattice spacing relationships and the electronic structure of h.c.p. zeta-phases based on silver, Philos. Mag. 8 (1961) 669–682. C.W. Fairhurst, J.B. Cohen, The crystal structure of two compounds found in dental amalgam: Ag2 Hg3 and Ag3 Sn, Acta Crystallogr. B 28 (1972) 371–378. N. Saunders, A.P. Miodownik, CALPHAD (calculation of phase diagrams): a comprehensive guide, Pergamon Materials Series 1, Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom, London, 1998. H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics: CALPHAD Method, Cambridge University Press, Cambridge, UK, 2007. B. Sundman, B. Jansson, J.O. Andersson, The thermo-calc databank system, CALPHAD 9 (1985) 153–190. O. Redlich, A.T. Kister, Thermodynamics of nonelectrolytic solutions. Algebraic representation of thermodynamic properties and the classification of solutions, Ind. Eng. Chem. 40 (1948) 84–88. B. Jansson, Evaluation of Paramters in Thermochemical Models Using Different Types of Experimental Data Simultaneously, Trita-Mac-0234, Division of Physical Metallurgy, Royal Institute of Technology, Stockholm, Sweden, 1984. Y. Du, R. Schmid-Fetzer, H. Ohtani, Thermodynamic assessment of the V-N system, Z. Metallkd. 88 (1997) 545–556.