Partial and integral enthalpies of mixing in the liquid Ag–In–Sn–Zn quaternary alloys

Thermochimica Acta xxx (2014) 1–9

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Partial and integral enthalpies of mixing in the liquid Ag–In–Sn–Zn quaternary alloys M.El Maniani, A. Sabbar * Equipe de Physico-Chimie des Matériaux et Nanomatériaux: Dépollution, Environnement et Développement Durable, Faculté des Sciences, Université Mohammed V- Agdal, Av. Ibn Batouta, B.P. 1014, Rabat, Morocco

A R T I C L E I N F O

A B S T R A C T

Article history: Received 21 May 2014 Received in revised form 25 July 2014 Accepted 29 July 2014 Available online xxx

The partial and integral enthalpies of mixing of liquid quaternary Ag–In–Sn–Zn alloys have been measured at 500
C along seven ternary sections: In0.450Sn0.450Zn0.100, In0.375Sn0.375Zn0.250, In0.333Sn0.333Zn0.334, In0.225Sn0.550Zn0.225, In0.100Sn0.800Zn0.100, In0.550Sn0.225Zn0.225 and In0.800Sn0.100Zn0.100. The measurements were carried out using a Calvet-type microcalorimeter and drop calorimetric technique. Additionally, the enthalpies of mixing of the liquid Ag–In–Sn–Zn have been calculated using the traditional Kohler, Muggianu, Toop and Hillert geometric models and compared to the experimental one. ã 2014 Elsevier B.V. All rights reserved.

Keywords: Integral enthalpies of mixing Partial enthalpies of mixing Lead free solders Liquid alloys Ag–In–Sn–Zn

1. Introduction Lead–tin solders are commonly used in electronic packaging due to their unique combination of electrical, chemical, physical, thermal and mechanical properties. However, lead and lead containing substances are among the top chemicals posing a considerable threat to human life and environment [1]. Over several years, much effort was put into developing alternative lead-free solder alloys. Although it is now widely agreed that there is no drop-in replacement for the standard Sn–Pb solders that have been used worldwide, a range of possible alternatives has been investigated. Because Sn is a common low melting temperature element that forms compounds with many metals of importance in electronic applications, it appears likely that any new alloy will also be Sn-based. Among many potential candidates, Ag–Sn, Cu–Sn, Zn–Sn, Ag–Cu–Sn . . . , Sn–Zn-based alloys were viewed as very promising candidates [2,3]. In 1994, McCormack and Jin [4,5] reported that the addition of In into the Sn–Zn alloys can positively contribute to the wetting characteristics of the alloys and lower sufficiently their melting temperatures. The quality and reliability of a solder joint is highly depending on phases and their microstructure formed during solidification. Although interfacial reactions between Sn–In and Sn–Zn binary

* Corresponding author. Tel.: +212 661409934. E-mail address: [email protected] (A. Sabbar). http://dx.doi.org/10.1016/j.tca.2014.07.028 0040-6031/ ã 2014 Elsevier B.V. All rights reserved.

alloys with those commonly used substrates have been examined, there are no similar studies regarding the interfacial reactions between substrates and In–Sn–Zn alloys. Among several pure metals with good conductivity, it is found that Ag is a suitable substrate to form only one layer intermetallic compounds (Ag3Sn) after chemical reactions with most Sn-based solders [6–8]. It is reported that the simple interfacial reaction between Ag and the solders is beneficial to the soldering joint reliability [6–8]. Recently, Chen et al. [9] have examined the interfacial reactions between In–Sn–Zn and Ag at 230
C. Therefore, knowledge of Ag–In–Sn–Zn quaternary system is important for the development of solder materials discussed above. Thus, information on thermochemistry and phase relation of these systems forms the base for a systematic alloy design which is desired to avoid complex and time consuming trial and error developing methods. Experimental thermochemical data such as mixing enthalpies are indispensable for the thermodynamic optimization of phase diagrams and the estimation of several physical properties, e.g. surface tension, viscosity and wettability. Recently, Rechchach et al. [10] have determined the enthalpies of mixing of the liquid In–Sn–Zn ternary alloys at 500
C over the entire composition range. More recently (2014), Boulouiz and Sabbar [11] have measured and calculated the enthalpies of mixing of Au–In–Sn–Zn quaternary alloys at 500
C. To our best knowledge, no data for the enthalpy of mixing of liquid alloys in the Ag–In–Sn–Zn quaternary system are available in the literature.

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M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

In the present work, the partial and the integral enthalpies of mixing of liquid quaternary Ag–In–Sn–Zn alloys were investigated at 500
C. Additionally, using the traditional geometric models of Kohler [12], Muggianu et al. [13], Toop [14] and Hillert [15], the integral enthalpy of mixing was calculated and compared to the experimental values. 2. Literature survey In the following, the thermodynamic information (enthalpy of mixing) concerning the limiting binary and ternary alloys have been recalled.

Flandorfer et al. [63] have measured the mixing enthalpy of liquid Ag–Sn alloys at 500, 700, 900, 1000, 1100 and 1250
C. 2.1.6. The Ag–Zn binary system Direct measurements of the enthalpy of mixing in liquid Ag–Zn alloys are not available in the literature, which is mainly due to the high vapour pressure of zinc. Nevertheless, reliable data about the enthalpy of formation of liquid alloys in this system were obtained indirectly by optimising the other thermodynamic properties available together with the phase equilibria by the CALPHAD technique [64]. 2.2. The ternary systems

2.1. The binary systems 2.1.1. The In–Sn binary system Several experimental investigations of the enthalpy of mixing of liquid In–Sn alloys can be found in the literature. They cover the entire composition range and a temperature range from 248 to 900
C [16–20]. All experimental data show negative values of enthalpy of mixing for the liquid In–Sn alloys. The enthalpy of mixing has been calculated by several authors [21–24]. Good agreement was obtained between calculated and experimental data. Recently, using direct-reaction calorimetry, Rechchach et al. [10] have determined the partial and the integral enthalpies of mixing of the liquid In–Sn alloys at 500
C and over the entire composition range. 2.1.2. The In–Zn binary system The enthalpy of mixing in the liquid In–Zn alloys has been measured using calorimetry [25–27] at about 450
C. The same measurements were investigated by EMF method [28–31] between 427 and 532
C. All the experimental data show positive values of enthalpy of mixing for the liquid In–Zn alloys. Lee [32], based on the above-mentioned experimental data [25–31], has calculated the enthalpy of mixing of liquid In–Zn alloys. The calculated and experimental results are in good agreement. 2.1.3. The Sn–Zn binary system Experimental investigations of the enthalpy of mixing of liquid Sn–Zn alloys can be found in the literature [33–39] between 422 and 546
C. Derived values of enthalpy of mixing were reported using EMF method [40–43]. All experimental data show positive values of enthalpy of mixing for the liquid Sn–Zn alloys. Several assessments of the enthalpy of mixing of liquid Sn–Zn alloys were reported [32,44,45] in comparison with all experimental data [33–43]. 2.1.4. The Ag–In binary system The enthalpies of mixing in the liquid Ag–In alloys have been measured by several authors [16,46–48] between 450 and 1007
C. The enthalpy of mixing varies with temperature, indicating a change in heat capacity. A thermodynamic assessment of this system was carried out by Korhonen and kivilahti [22] in comparison with some experimental data [16,46,48]. Later, Moser et al. [49] have calculated the enthalpy of mixing in the liquid phase at 727
C. Fair agreement was obtained between calculated [49] and experimental data [46,48]. 2.1.5. The Ag–Sn binary system Using several techniques (calorimetry, potentiometry, vapour pressure), the enthalpies of mixing of liquid Ag–Sn alloys have been measured by several authors [50–56] from 554 to 1100
C over a very large composition range. A good agreement was obtained with all experimental data. The mixing enthalpies of molten Ag–Sn alloys have been assessed [57–62]. Recently,

2.2.1. The In–Sn–Zn ternary system The enthalpies of mixing of liquid In–Sn–Zn alloys have already been measured by some authors. Fiorani et al. [65] have measured the partial and the integral enthalpies of mixing in the liquid In– Sn–Zn alloys following the three isopletic cuts: xIn/xSn = 1/1 at 447
C, xSn/xZn = 1/1 at 447
C and xIn/xZn = 1/1 at 483
C. Later, Anres et al. [66] have investigated by direct reaction calorimetry the enthalpies of mixing in the liquid In–Sn–Zn ternary alloys. Their measurements were explored at 440 and 634
C following the sections xIn/xSn = 1/3, 1/1, 3/1 and xZn/xIn = 1/3, 1/1. Cui et al. [67] have calculated the partial mixing enthalpies of In, Sn and Zn at 447, 483 and 447
C respectively in comparison with the experimental data reported by Fiorani et al. [65]. There is no good agreement between the calculated and experimental data. Xie et al. [68], using CALPHAD technique, have calculated the mixing enthalpies of In–Sn–Zn ternary liquid alloys at 439
C. The calculated results are in good agreement with the experimental data reported by Anres et al. [66]. Moelans et al. [69], using CALPHAD method, have assessed the mixing enthalpy at 441 and 634
C for the section xIn/xSn = 1/3 in comparison with experimental data reported previously by Anres et al. [66]. Recently, the mixing enthalpy of the liquid In–Sn–Zn alloys has been measured at 500
C using a drop method calorimetry by Rechchach et al. [10]. The measurements were examined following seven sections: xIn/ xSn = 0.851/0.149, 0.667/0.333, 0.501/0.499, 0.336/0.664, 0.152/ 0.848 and xIn/xZn = 0.702/0.298, 0.519/0.481. 2.2.2. The Ag–In–Sn ternary system The enthalpies of mixing of liquid Ag–In–Sn alloys have been measured by calorimetry by Gather et al. [70] following the four isopletic cuts: xIn/xSn = 1/4 at 893
C, xIn/xSn = 2/3 at 893
C, xIn/ xSn = 3/2 at 980
C and xIn/xSn = 4/1 at 980
C. Recently, Liu et al. [71] have calculated the enthalpy of mixing in the liquid phase at the same vertical sections investigated by Gather et al. [70]. The results indicate that there is basic agreement between the experimental and calculated results. 2.2.3. The Ag–Sn–Zn ternary system EMF method was applied by Karlhuber et al. [72] to derive the enthalpy of mixing of this system at 627
C following the three sections: xAg/xSn = 1/3, 1/1 and 3/1. Peng et al. [73], using four different models developed by Kohler [12], Toop [13], Mugianu [14] and Hillert [15], have calculated the mixing enthalpy of liquid Ag–Sn–Zn following the same sections investigated by Karlhuber et al. [72]. The calculated values are more negative. Later, Knott et al. [74] have measured the integral enthalpies of mixing in the liquid phase at 700
C along cross-sections with molar ratios Ag: Sn = 1:3, 1:1, 3:1 and Zn mole fractions from 0 to about 0.4. Very recently, Vassilev et al. [75] have calculated the enthalpy of mixing of the liquid Ag–Sn–Zn alloys at 700
C with the same molar ratios investigated by Knott et al. [74]. Good agreement between calculated and newer experimental results [74] is obtained.

M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

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2.2.4. The Ag–In–Zn ternary system For this ternary system, no experimental data on the thermodynamic properties is available.

The systematic errors are mainly caused by parasitic heat flows, base line problems at signal integration and dropping and mixing problems. One can estimate that the overall error is 250 J/mol.

2.3. The quaternary Ag–In–Sn–Zn system

4. Results and discussion

No experimental data on the thermodynamic properties can be found for this quaternary system.

4.1. Experimental results

3. Experimental procedure The calorimetric measurements were carried out in a Calvettype microcalorimeter (SETARAM, Lyon, France; thermopile with more than 200 thermocouples, wire wound resistance furnace, automatic drop device for up to 30 drops, control and data evaluation with LabView HiQ as described by Flandorfer et al. [76]). To prevent oxidation all measurements were performed under Ar flow (approx. 30 cm3/min). At the end of each series the calorimeter was calibrated by five or six drops (between 30 and 50 mg each) of NIST standart a-Al2O3 (National Institute of Standards and Technology, Gaithersburg, MD). The samples were prepared from In rods (99.999%, ASARCO, South Plainfield, NJ), Sn rods (99.998%, Alfa Johnson Matthey, Karlsruhe, Germany), Zn (99.999%, ASARCO, South Plainfield, NJ) and Ag shot (99.98%, ÖGUSSA, Vienna, Austria) which was heated in a carbon crucible at 700
C for 10 min for surface cleaning. In, Sn and Zn were used without further purification. For the quaternary Ag–In–Sn–Zn, the enthalpies of mixing of 140 molten samples have been measured along seven sections (A– G, Table 1). Pieces of pure Ag (20–50 mg) were dropped into 460– 530 mg of molten InxSnyZnz. The time interval between individual drops was usually 40 min and the heat flow acquisition interval was about 0.73 s. Obtained signals were recorded, integrated and quantified applying the calorimeter constant evaluated by calibration. The measured enthalpy (integrated heat flow at constant pressure) is:

DHdrop ¼ ni ½Hið1Þ; FT  HiðsÞ; DT  þ Dreaction;i ni is the number of moles of the dropped element i, FT = furnace temperature, and DT = drop temperature (initial temperature). The relative enthalpy Hi(1),FT  Hi(s),DT was calculated using the polynomials for the thermodynamic data of pure elements in the SGTE data base [77]. For the respective temperatures FT and DT, the average of the values for each drop of a run was taken because their scattering was low enough and not influence the accuracy of the method. The values used for all the calculations are FT = 773 K and DT = 298 K. Because of the rather small masses added, the partial enthalpy DH m;i of the dropped metal i can be considered as:

DH m;i 

DHreaction;i ni

The integral molar enthalpy of mixing DmixH was calculated by: P ðDHter þ i DHreaction;i Þ P Dmix H ¼ nter þ i ni nter is the molar amount and DHter the integral enthalpy of the metals (In, Sn and Zn) propounded in the crucible. Random errors as well as systematic errors of calorimetry depend on the construction of the calorimeter, calibration procedure, signal integration and “chemical errors”, e.g. incomplete reactions or impurities. Considering many calibration measurements done by dropping NIST standard sapphire, the standard deviation can be estimated to be less than 1% for the HT1000.

Seven measurements have been performed at different cross sections of In:Sn:Zn (A–G) (Fig. 1). All the experimental data of the measurement sections in the Ag–In–Sn–Zn system can be found in Table 1. This table contains information on the exact measurement, starting amounts of In, Sn and Zn, added amounts of Ag, heat effect and the partial and integral enthalpies of mixing of the liquid alloys. The heat effect mentioned in Table 1 is obtained by dividing the measured enthalpy DHdrop by the number of moles of dropped Ag. Heat effect ¼

DHdrop nAg

The starting values of the integral enthalpy of mixing for the seven different ternary In–Sn–Zn compositions are taken from our previous work [10] performed at the same experimental temperature (500
C). As an example, Fig. 2 shows partial molar enthalpies of mixing along section E (pure Ag dropped into In0.100Sn0.800Zn0.100) and section G (pure Ag dropped into In0.800Sn0.100Zn0.100), respectively. It can be seen that a decrease in the partial enthalpy of Ag is determined, as amount of Ag increases. The values obtained for Snrich side (section E) are more endothermic than those reported in the In-rich region (section G). Fig. 3 illustrates, for the same sections (E and G), the experimental results of integral molar enthalpies of mixing. As in the case of partial molar quantity, a decrease in the integral enthalpy is noted, as amount of Ag increases. For the quaternary section Ag–In0.100Sn0.800Zn0.100, at low compositions of silver (up to 25 at% Ag), the mixing enthalpies of the liquid phase show slightly positive values, while the results obtained for the section Ag–In0.800Sn0.100Zn0.100 show that the endothermic domain of the mixing enthalpies is very limited, up to 0.11 at% Ag. The same behaviour was obtained for the various studied sections (A–G). The positive domain of the mixing enthalpies varies according to the studied isopleths (Table 2). From the results obtained for the seven sections, it can be noted (Table 2) that the large endothermic domain of the integral enthalpies of mixing (0  xAg  0.25) is obtained for the Sn-rich section (E) with 8 DmixH = 2100 J/mol (the less exothermic value) at xAg = 0.5 (See table 2) while the limited positive domain of the integral enthalpies of mixing (0  xAg  0.11) is reported for the In-rich section (G) with DmixH = 4300 J/mol (the more exothermic value) at xAg = 0.5 (See table 2). For the seven studied sections, all the quaternary alloys are in liquid phase at the experimental temperature (500
C). 4.2. Calculated results Four different extrapolation models were used to calculate the enthalpy of mixing in the quaternary Ag–In–Sn–Zn system. The predicted values were compared with the experimental values. The models from Kohler [12] and Muggianu et al. [13] use simple symmetric extrapolation models based on binary data, whereas Toop [14] and Hillert [15] models are an asymmetric models. A quaternary system contains six binary systems, and the information of all these binary systems should be known before using the geometric models.

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Table 1 Partial and integral molar enthalpies of mixing in the liquid Ag–In–Sn–Zn alloys; initial state for DmixH: pure liquid metals at 500
C. Mole dropped n(Ag)

Heat effecta

Partial enthalpy

J mol1

Mole fraction xAgb

Integral enthalpy xIn

xSn

xAg

DmixH

Section A; starting amount:n(In) = 2.1025 mmol;n(Sn) = 2.0975 mmol;n(Zn) = 0.4627 mmol – – – – 0.1642 3,409 0.0170 2,894 0.1693 3,416 0.0504 3,473 0.1793 3,506 0.0829 4,096 0.1816 3,530 0.1144 4,215 0.1837 3,464 0.1441 4,793 0.1839 3,367 0.1720 5,342 0.1848 3,293 0.1982 5,835 0.2238 3,897 0.2254 6,238 0.2266 3,808 0.2533 6,845 0.2294 3,737 0.2796 7,365 0.2316 3,713 0.3044 7,623 0.2383 3,753 0.3280 7,904 0.2582 4,001 0.3511 8,153 0.2697 4,058 0.3741 8,604 0.2809 4,128 0.3964 8,956 0.2822 4,079 0.4177 9,198 0.3006 4,230 0.4381 9,577 0.3028 4,126 0.4578 10,025 0.3163 4,279 0.4766 10,123 0.3241 4,155 0.4948 10,830

0.4509 0.4356 0.4208 0.4062 0.3925 0.3795 0.3673 0.3558 0.3428 0.3306 0.3191 0.3082 0.2978 0.2873 0.2771 0.2672 0.2580 0.2488 0.2402 0.2318 0.2238

0.4498 0.4345 0.4198 0.4053 0.3915 0.3786 0.3664 0.3549 0.3420 0.3298 0.3183 0.3075 0.2971 0.2866 0.2765 0.2666 0.2574 0.2482 0.2396 0.2313 0.2233

0.0000 0.0340 0.0667 0.0991 0.1296 0.1585 0.1855 0.2110 0.2398 0.2669 0.2924 0.3164 0.3395 0.3628 0.3854 0.4074 0.4279 0.4483 0.4673 0.4859 0.5037

591 472 338 185 36 125 292 465 676 896 1,121 1,342 1,563 1,796 2,038 2,285 2,524 2,775 3,026 3,273 3,534

Section B; starting amount:n(In) = 1.7360 mmol;n(Sn) = 1.7286 mmol;n(Zn) = 1.1726 mmol – – – – 0.1698 3,108 0.0177 5,472 0.1781 3,116 0.0526 6,288 0.1869 3,178 0.0866 6,773 0.1873 3,089 0.1191 7,289 0.1934 3,092 0.1498 7,795 0.2057 3,255 0.1798 7,954 0.2060 3,112 0.2086 8,675 0.2135 3,160 0.2360 8,979 0.2198 3,169 0.2623 9,359 0.2245 3,129 0.2875 9,842 0.2269 3,081 0.3114 10,200 0.2339 3,143 0.3341 10,343 0.2388 3,123 0.3560 10,701 0.2410 3,197 0.3768 10,514 0.2494 3,242 0.3966 10,778 0.2560 3,213 0.4158 11,231 0.2564 3,159 0.4341 11,459 0.2629 3,278 0.4515 11,314 0.3333 4,066 0.4701 11,579 0.3514 4,264 0.4900 11,644

0.3744 0.3611 0.3482 0.3357 0.3239 0.3126 0.3015 0.2911 0.2810 0.2713 0.2621 0.2535 0.2451 0.2371 0.2295 0.2222 0.2152 0.2085 0.2022 0.1946 0.1872

0.3723 0.3596 0.3468 0.3342 0.3225 0.3113 0.3002 0.2898 0.2798 0.2702 0.2610 0.2524 0.2440 0.2361 0.2286 0.2213 0.2142 0.2076 0.2013 0.1938 0.1864

0.0000 0.0353 0.0698 0.1034 0.1347 0.1649 0.1947 0.2225 0.2494 0.2752 0.2998 0.3230 0.3453 0.3667 0.3868 0.4064 0.4253 0.4430 0.4600 0.4802 0.4999

1,845 1,587 1,306 1,014 724 427 127 177 481 786 1,093 1,395 1,690 1,984 2,256 2,528 2,804 3,071 3,323 3,631 3,935

Section C; starting amount:n(In) = 1.6806 mmol;n(Sn) = 1.6790 mmol;n(Zn) = 1.6809 mmol – – – – 0.1651 2,703 0.0159 7,358 0.1727 2,773 0.0473 7,680 0.1860 2,870 0.0785 8,300 0.1872 2,842 0.1089 8,553 0.1948 2,894 0.1380 8,880 0.1986 2,848 0.1660 9,396 0.2032 2,824 0.1929 9,841 0.2119 2,917 0.2188 9,969 0.2215 3,008 0.2442 10,151 0.2408 3,205 0.2695 10,426 0.2571 3,345 0.2949 10,725 0.2623 3,303 0.3196 11,145 0.2624 3,318 0.3429 11,091 0.2729 3,387 0.3650 11,325 0.2837 3,443 0.3865 11,600 0.2844 3,416 0.4070 11,723 0.3031 3,622 0.4268 11,784 0.3668 4,347 0.4478 11,884 0.3896 4,613 0.4698 11,895 0.4024 4,795 0.4910 11,818

0.3334 0.3228 0.3125 0.3020 0.2922 0.2826 0.2735 0.2647 0.2562 0.2478 0.2393 0.2309 0.2228 0.2153 0.2081 0.2010 0.1944 0.1878 0.1804 0.1732 0.1663

0.3331 0.3225 0.3122 0.3017 0.2919 0.2824 0.2732 0.2645 0.2559 0.2476 0.2391 0.2306 0.2226 0.2151 0.2079 0.2008 0.1942 0.1876 0.1802 0.1730 0.1661

0.0000 0.0317 0.0628 0.0941 0.1236 0.1523 0.1797 0.2060 0.2316 0.2567 0.2822 0.3076 0.3317 0.3541 0.3760 0.3971 0.4170 0.4367 0.4589 0.4806 0.5013

2,345 2,037 1,725 1,390 1,066 740 413 85 240 564 902 1249 1,593 1,913 2,231 2,549 2,850 3,153 3,497 3,834 4,152

Section D; starting amount:n(In) = 0.9807 mmol;n(Sn) = 2.3942 mmol;n(Zn) = 0.9830 mmol – – – –

0.2250

0.5494

0.0000

1,695

mmol

DH m; Ag J mol1

J mol1

M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

5

Table 1 (Continued) Mole dropped n(Ag)

Heat effecta

Partial enthalpy

J mol1

Mole fraction xAgb

DH m; Ag

xIn

xSn

xAg

DmixH

mmol 0.1642 0.1772 0.1794 0.1810 0.1820 0.1841 0.2037 0.2051 0.2062 0.2091 0.2119 0.2154 0.2270 0.2294 0.2301 0.2559 0.2658 0.2816 0.2819 0.2833

3,211 3,343 3,259 3,169 3,096 3,091 3,299 3,263 3,129 3,168 3,157 2,949 3,229 3,240 3,180 3,560 3,607 3,758 3,710 3,712

0.0182 0.0545 0.0897 0.1227 0.1537 0.1827 0.2113 0.2395 0.2658 0.2906 0.3141 0.3365 0.3581 0.3789 0.3986 0.4181 0.4377 0.4569 0.4753 0.4926

3,974 4,654 5,354 6,017 6,511 6,730 7,327 7,614 8,348 8,379 8,629 9,832 9,304 9,405 9,706 9,611 9,957 10,183 10,363 10,422

0.2169 0.2087 0.2010 0.1938 0.1871 0.1807 0.1742 0.1681 0.1623 0.1569 0.1518 0.1469 0.1420 0.1375 0.1332 0.1287 0.1244 0.1201 0.1161 0.1123

0.5294 0.5095 0.4907 0.4732 0.4568 0.4413 0.4253 0.4103 0.3963 0.3831 0.3705 0.3586 0.3468 0.3356 0.3251 0.3142 0.3036 0.2932 0.2834 0.2742

0.0363 0.0726 0.1067 0.1387 0.1686 0.1968 0.2259 0.2531 0.2786 0.3027 0.3256 0.3473 0.3688 0.3891 0.4082 0.4281 0.4473 0.4664 0.4842 0.5009

1,490 1,258 1,015 763 511 265 10 277 552 814 1,071 1,353 1,615 1,865 2,110 2,362 2,618 2,879 3,129 3,365

Section E; starting amount:n(In) = 0.4669 mmol;n(Sn) = 3.7320 mmol;n(Zn) = 0.4663 mmol – – – – 0.1628 3,881 0.0169 266 0.1726 3,983 0.0504 489 0.1812 4,036 0.0834 1,290 0.1892 4,137 0.1156 1,695 0.1961 4,254 0.1467 1,871 0.1978 4,145 0.1764 2,607 0.1991 4,011 0.2043 3,421 0.2350 4,667 0.2326 3,705 0.2374 4,569 0.2613 4,317 0.2383 4,458 0.2881 4,859 0.2393 4,398 0.3132 5,190 0.2450 4,326 0.3368 5,905 0.2479 4,329 0.3592 6,103 0.2506 4,316 0.3805 6,338 0.2509 4,210 0.4004 6,783 0.2523 4,134 0.4192 7,179 0.2571 4,184 0.4371 7,292 0.2874 4,605 0.4549 7,540 0.3135 4,922 0.4734 7,864 0.3342 4,989 0.4920 8,638

0.1001 0.0967 0.0934 0.0901 0.0869 0.0839 0.0810 0.0783 0.0753 0.0725 0.0700 0.0675 0.0652 0.0630 0.0610 0.0590 0.0572 0.0555 0.0536 0.0518 0.0499

0.8000 0.7730 0.7463 0.7202 0.6948 0.6704 0.6474 0.6257 0.6020 0.5798 0.5591 0.5398 0.5213 0.5039 0.4874 0.4719 0.4573 0.4433 0.4287 0.4138 0.3990

0.0000 0.0337 0.0671 0.0997 0.1314 0.1620 0.1908 0.2178 0.2474 0.2752 0.3011 0.3253 0.3483 0.3701 0.3908 0.4101 0.4283 0.4458 0.4641 0.4827 0.5012

787 769 726 655 572 486 380 253 103 60 231 403 591 776 958 1,142 1,329 1,511 1,710 1,924 2,164

Section F; starting amount:n(In) = 2.4679 mmol;n(Sn) = 1.0121 mmol;n(Zn) = 1.009 mmol – – – – 0.1626 2,742 0.0175 6,640 0.1631 2,650 0.0513 7,258 0.1761 2,764 0.0841 7,808 0.1810 2,769 0.1163 8,212 0.1875 2,782 0.1472 8,670 0.1968 2,873 0.1772 8,905 0.2006 2,819 0.2061 9,456 0.2120 2,852 0.2340 10,052 0.2169 2,858 0.2611 10,327 0.2201 2,818 0.2867 10,700 0.2219 2,776 0.3109 10,997 0.2380 2,873 0.3344 11,434 0.2452 2,964 0.3574 11,419 0.2577 3,007 0.3797 11,838 0.2579 2,959 0.4011 12,034 0.2583 2,911 0.4210 12,238 0.2632 2,922 0.4398 12,405 0.2642 2,912 0.4577 12,481 0.2757 3,071 0.4748 12,366 0.3477 3,885 0.4932 12,332

0.5498 0.5305 0.5125 0.4944 0.4771 0.4604 0.4441 0.4286 0.4134 0.3989 0.3852 0.3723 0.3594 0.3470 0.3349 0.3236 0.3130 0.3029 0.2933 0.2840 0.2731

0.2255 0.2176 0.2102 0.2028 0.1957 0.1888 0.1821 0.1758 0.1696 0.1636 0.1580 0.1527 0.1474 0.1423 0.1373 0.1327 0.1284 0.1242 0.1203 0.1165 0.1120

0.0000 0.0349 0.0676 0.1005 0.1320 0.1624 0.1920 0.2202 0.2479 0.2743 0.2992 0.3226 0.3461 0.3687 0.3908 0.4114 0.4306 0.4490 0.4663 0.4833 0.5031

1,724 1,432 1,137 822 505 184 137 462 803 1,137 1,465 1,784 2,119 2,439 2,768 3,081 3,381 3,673 3,950 4,217 4,529

Section G; starting amount:n(In) = 3.5867 mmol;n(Sn) = 0.4488 mmol;n(Zn) = 0.4481 mmol – – – – 0.1700 3,175 0.0183 4,914 0.1736 3,127 0.0538 5,577 0.1843 3,198 0.0882 6,248

0.8000 0.7707 0.7430 0.7157

0.1001 0.0964 0.0930 0.0896

0.0000 0.0365 0.0712 0.1053

827 618 395 151

Integral enthalpy J mol1

J mol1

6

M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

Table 1 (Continued) Mole dropped n(Ag)

Heat effecta

Partial enthalpy

J mol1

Mole fraction xAgb

DH m; Ag

xIn

xSn

xAg

DmixH

mmol 0.1886 0.2015 0.2058 0.2067 0.2127 0.2139 0.2141 0.2257 0.2379 0.2429 0.2454 0.2471 0.2483 0.2594 0.2743 0.2759 0.2784

3,224 3,388 3,291 3,236 3,214 3,115 3,035 3,126 3,191 3,210 3,107 3,056 3,014 3,092 3,245 3,324 3,300

0.1216 0.1539 0.1852 0.2146 0.2424 0.2688 0.2935 0.3171 0.3404 0.3629 0.3843 0.4044 0.4234 0.4416 0.4596 0.4769 0.4933

6,500 6,780 7,602 7,936 8,486 9,027 9,421 9,744 10,181 10,383 10,936 11,224 11,458 11,674 11,765 11,548 11,741

0.6897 0.6640 0.6396 0.6169 0.5951 0.5747 0.5557 0.5369 0.5184 0.5008 0.4843 0.4686 0.4539 0.4395 0.4252 0.4117 0.3990

0.0863 0.0831 0.0800 0.0772 0.0745 0.0719 0.0695 0.0672 0.0649 0.0627 0.0606 0.0586 0.0568 0.0550 0.0532 0.0515 0.0499

0.1378 0.1699 0.2004 0.2288 0.2560 0.2815 0.3054 0.3288 0.3519 0.3739 0.3946 0.4142 0.4326 0.4506 0.4685 0.4853 0.5013

91 340 607 867 1,136 1,406 1,672 1,945 2,228 2,505 2,784 3,057 3,321 3,586 3,852 4,096 4,333

a b

Integral enthalpy J mol1

J mol1

The heat effect is the enthalpy absorbed in a drop experiment with initial TAg = 298 K per mole of dropped Ag. Average value before and after each drop.

The various predictive extensions from the binary to quaternary A–B–C–D system are shown below (where xA, xB, xC and xD are the molar fractions in the quaternary A–B–C–D system). Kholer model [12]:   xA xA Dmix HABCD ¼ ðxA þ xB Þ2 Dmix HAB ; xA þ xB  xA þ xB  xA xC ; þðxA þ xC Þ2 Dmix HAC xA þ xC xA þ xC  xA xD 2 ; þðxA þ xD Þ Dmix HAD xA þ xD xA þ xD xB xC ; þðxB þ xC Þ2 Dmix HBC xB þ xC xB þ xC  xB xD ; þðxB þ xD Þ2 Dmix HBD xB þ xD xB þ xD  xC xD ; þðxC þ xD Þ2 Dmix HCD xC þ xD xC þ xD

Muggianu et al. model [13]: 4xA xB D HAB ð1 þ xA  xBÞð1 þ xB  xA Þ mix  1 þ xA  xB 1 þ xB  xA ;  2 2   4xA xC 1 þ xA  xC 1 þ xC  xA ; Dmix HAC þ ð1 þ xA  xC Þð1 þ xC  xA Þ 2 2   4xA xD 1 þ xA  xD 1 þ xD  xA ; Dmix HAD þ ð1 þ xA  xD Þð1 þ xD  xA Þ 2 2   4xB xC 1 þ xB  xC 1 þ xC  xB ; Dmix HBC þ ð1 þ xB  xC Þð1 þ xC  xB Þ 2 2   4xB xD 1 þ xB  xD 1 þ xD  xB ; Dmix HBD þ ð1 þ xB  xD Þð1 þ xD  xB Þ 2 2   4xC xD 1 þ xC  xD 1 þ xD  xC ; Dmix HCD þ ð1 þ xC  xD Þð1 þ xD  xC Þ 2 2

Dmix HABCD ¼

Zn 0,0 0,1

1,0 0,9

0,2

0,8

0,3

0,7

0,4

0,6

0,5

0,5

0,6

0,4

C 0,7

B

F

0,2

G

0,9

0,3

D

0,8

E

A

0,1

1,0

In

0,0

0,0 0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Sn

Fig. 1. Measured sections in the quaternary Ag–In–Sn–Zn system at 500
C. A–G are the starting ternary InxSnyZnz compositions.

Fig. 2. Partial molar enthalpies of mixing at 500
C in liquid Ag–In–Sn–Zn alloys along section E (pure Ag dropped into In0.100Sn0.800Zn0.100) and G (pure Ag dropped into In0.800Sn0.100Zn0.100). Standard states: pure liquid metals.

M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

7

Fig. 3. Integral molar enthalpies of mixing at 500
C in liquid Ag–In–Sn–Zn alloys along section E (pure Ag dropped into In0.100Sn0.800Zn0.100) and G (pure Ag dropped into In0.800Sn0.100Zn0.100). Standard states: pure liquid metals.

Table 2 Endothermic domain of DmixH and DmixH-values at xAg = 0.5 for the seven studied isopleths. Isopleth

Positive domain of DmixH

DmixH (J/mol) at xAg = 0.5

A: Ag–In0.450Sn0.450Zn0.100 B: Ag–In0.375Sn0.375Zn0.250 C: Ag–In0.333Sn0.333Zn0.334 D: Ag–In0.225Sn0.550Zn0.225 E: Ag–In0.100Sn0.800Zn0.100 F: Ag–In0.550Sn0.225Zn0.225 G: Ag–In0.800Sn0.100Zn0.100

0  xAg  0.13 0  xAg  0.20 0  xAg  0.21 0  xAg  0.20 0  xAg  0.25 0  xAg  0.17 0  xAg  0.11

3500 3950 4150 3350 2100 4500 4300

Muggianu models give more exothermic values than those of the asymmetric Toop and Hillert models. Generally, in comparison xB xC with the experimental results, the Toop’s and Hillert’s asymmetric Dmix HABCD ¼ ðxB þ xC Þ2 Dmix HBC ; xB þ xC  xB þ xC  models lead to a better prediction of enthalpy of mixing than the xB xD ; þðxB þ xD Þ2 Dmix HBD two symmetric models (Kohler and Muggianu) except for the SnxB þ xD xB þ xD  rich section E (In0.100Sn0.800Zn0.100–Ag) where the symmetric xC xD xB ; D HAB ðxA ; 1  xA Þ models yield to a better results. þ þðxC þ xD Þ2 Dmix HCD xC þ xD xC þ xD 1  xA mix Additionally, if one takes the root mean square deviation xC xD D HAC ðxA ; 1  xA Þ þ D HAD ðxA ; 1  xA Þ þ corresponding to experimental results for each traditional model, ð1  xA Þ mix ð1  xA Þ mix i.e. Hillert model [15]: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N x x X 1u Dmix HABCD ¼ B C Dmix HBC ðnBC ; nCB Þ t ðD H ¼  DMix Hexp;i Þ2 S nBC nCB N i¼1 Mix cal;i xB xD x x Dmix HBD ðnBD ; nDB Þ þ C D Dmix HCD ðnCD ; nDC Þ þ Toop model [14]:



nBD nDB



nCD nDC

xB D H ðx ; 1  xA Þ ð1  xA Þ mix AB A xC D HAC ðxA ; 1  xA Þ þ ð1  xA Þ mix xD D HAD ðxA ; 1  xA Þ þ ð1  xA Þ mix

þ

Where vij = (1 + xi - xj)/2 and ?ji = (1 + xj - xi)/2. For our calculation we used the data of Hultgreen et al. [78] for the Ag–In system, Flandorfer et al. [63] for the Ag–Sn system, Gomez-Acebo [64] for the Ag–Zn system, Rechchach et al. [10] for the In–Sn system and Hultgreen et al. [78] for the Sn–Zn and In–Zn systems. Fig. 4 shows the calculated integral enthalpies of mixing in comparison with the experimental values. The experimental results are also included in Fig. 4 for comparison. It can be seen that, for all measured sections (A–G), the symmetric Kohler and

Where DmixHcal,i and DmixHexp,i represent the integral enthalpies of mixing at a fixed composition “i” for a theoretical model and an experimental results, respectively, while N is the total number of investigated alloys. According to the calculation, the S-values for the Kohler, Muggianu, Toop and Hillert models are 84, 60, 30 and 31, respectively. From these S-values, Toop and Hillert asymetric models give the minimum values (30 and 31 respectively). One can conclude that the Ag–In–Sn–Zn quaternary system can be considered as an asymmetric system. Acknowledgements We would like to thank Prof. H. Flandorfer and Prof. H. Ipser who allowed us to realize the calorimetric measurements in the Institute of Inorganic Chemistry (material chemistry group) at Vienna University.

8

M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

Fig. 4. Experimental and calculated integral enthalpy of mixing in liquid Ag–In–Sn–Zn using the four geometric models (Kohler, Muggianu, Toop and Hillert).

M.E. Maniani, A. Sabbar / Thermochimica Acta xxx (2014) 1–9

References [1] Directive 2002/95/EC, Directive 2002/95/EC of the European Parliament and of the Council of 27 January 2003 on the restriction of the use of certain Hazardous Substances in electrical and electronic equipment ROHS, Official J. Eur. Union L37 (2003) 19–23. [2] K. Suganuma, S.-J. Kim, K.-S. Kim, JOM 61 (2009) 64–71. [3] S. Kim, K.-S. Kim, S.-S. Kim, K. Suganuma, J. Electron. Mater. 38 (2009) 266–272. [4] M. McCormack, S. Jin, J. Electron. Mater. 23 (1994) 635–640. [5] M. McCormack, S. Jin, J. Electron. Mater. 23 (1994) 715–720. [6] T. Lauril, V. Vuorinen, J.K. Kivialahti, Mater. Sci. Eng. R 49 (2005) 1. [7] Y.T. Huang, T.H. Chuang, Z. Metallkd. (12 2000) 1002. [8] M.D. Cheng, S.S. Wang, T.H. Chuang, J. Electron. Mater. 31 (3) (2002) 171. [9] Sin-wen Chen, Ching-feng Yang, Hsin-jay Wu, Ru-B0 Chang, Chia-ming Hsu, Mater. Chem. Phys. 132 (2012) 481–487. [10] M. Rechchach, A. Sabbar, H. Flandorfer, H. Ipser, Thermochim. Acta 502 (2010) 66–72. [11] A. Boulouiz, A. Sabbar, Thermochim. Acta 575 (2014) 151–158. [12] F. Kohler, Monatsh. Chem. 91 (1960) 738. [13] Y.M. Muggianu, M. Gambino, J.P. bros, J. Chim. Phys. 72 (1975) 83. [14] G.N. Toop, Trans Met. Soc. AIME 233 (1965) 850. [15] M. Hillert, CALPHAD 4 (1980) 1. [16] O.J. Kleppa, J. Phys. Chem. 60 (1956) 846. [17] F.E. Wittig, P. Scheidt, Z. Phys. Chem. 28 (1961) 120–142. [18] A. Yazawa, T. Kawashima, K. Itagaki, J. Jpn. Inst. Met. 32 (1968) 1281–1287. [19] J.P. Bros, M. Laffitte, J. Chem. Thermodyn. 2 (1970) 151–152. [20] C. Luef, H. Flandorfer, H. Ipser, Thermochim. Acta 417 (2004) 47–57. [21] B.-J. Lee, C.-S. Oh, J.-H. Shim, J. Electron. Mater. 25 (1996) 983–991. [22] T.M. Korhonen, J.K. Kivilahti, J. Electron. Mater. 27 (1998) 149–158. [23] A. Schlieper, R. Blachnik, Z. Metallkd. 91 (2000) 24–34. [24] N. David, K. El Aissaoui, J.M. Fiorani, J. Hertz, M. Vilasi, Thermochim. Acta 413 (2004) 127–137. [25] W. Oelsen, P. Zühlke, Arch. Eisenhüttenwes 27 (1956) 743. [26] O.J. Kleppa, Acta Metall. 6 (1958) 225. [27] F.E. Wittig, E. Müller, Z. Metallkd. 51 (1960) 226. [28] W.J. Svirbely, S.M. Selis, J. Am. Chem. Soc. 75 (1953) 1532. [29] R.W. Bohl, V.D. Hildebrandt, J. Am. Chem. Soc. 79 (1957) 2711. [30] Z. Moser, Rev. Rom. Chim. 16 (1971) 327. [31] D. Ferro, B.M. Nappi, V. Piacente, P.L. Cignini, High Temp. Sci. 10 (1978) 131. [32] B.-J. Lee, CALPHAD 20 (4) (1996) 471–480. [33] O.J. Kleppa, J. Phys. Chem. 59 (1955) 354. [34] W. Oelsen, Z. Metallkd. 48 (1957) 1–8. [35] E. Schürmann, H. Träger, Arch. Eisenhüttenwes 32 (1961) 397–408. [36] Z. Moser, K. Rzyman, S. Randzio, Bull. Acad. Pol. Sci. Tech. 35 (1987) 461. [37] B. Dobovisek, B. Straus, Rudarsko Met. Zbornik 3 (1960) 273. [38] M. Genot, R. Hagege, Compt. Rend. Acad. Sci. Fr. 25 (1960) 2901. [39] K. Itagaki, A. Yazawa, J. Jpn. Inst. Met. 39 (1975) 880.

[40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78]

9

W. Ptak, Arch. Hutnictwa 5 (1960) 169. K. Sano, K. Okajima, S. Tatsuo, Mem. Fac. Eng. Nagoya Univ. 5 (1953) 299. M. Fiorani, V. Valenti, Gazz. Chim. Ital. 85 (1955) 607. E. Scheil, E.D. Müller, Z. Metallkd. 53 (1962) 389. A. Bourkba, J.M. Fiorani, C. Naguet, J. Hertz, Z. Metallkd. 87 (1996) 10. H. Ohtani, M. Miyashita, K. Ishida, J. Jpn. Inst. Met. 63 (6) (1999) 685–694. R. Beja, M. Laffitte, C. R. Acad. Sci. 267C (1968) 123. C.B. Alcock, R. Sridhar, R.C. Svedberg, Acta Metall. 17 (1969) 839–844. R. Castanet, Y. Clair, M. Laffitte, J. Chim. Phys. 67 (4) (1970) 789–793. Z. Moser, W. Gasior, J. Pstrus, W. Zakulski, I. Ohnuma, X.J. Liu, Y. Inohana, K. Ishida, J. Electron. Mater. 30 (9) (2001) 1120–1128. M. Kawakami, Sci. Rep. Tohoku Univ. 19 (1930) 521–549. O.J. Kleppa, Acta Metall. 3 (1955) 255–259. F.E. Wittig, E. Gehring, Z. Nat. A 18 (1963) 351–362. G.H. Laurie, A.H. Morris, J.N. Pratt, Trans AIME 236 (1966) 1390–1395. K. Itagaki, A. Yazawa, J. Jpn. Inst. Met. 32 (1968) 1294–1300. R. Castanet, M. Laffitte, C. R. Acad. Sci. C 267 (1968) 204–206. L.J. Rakotomavo, M. Gaune-Escard, J.P. Bros, P. Gaune, Ber. Bunsenges. Phys. Chem. 88 (1984) 663–670. I. Karakaya, W.T. Thompson, Bull. Alloy Phase Diagr. 8 (4) (1987) 340–347. P.-Y. Chevalier, Thermochim. Acta 136 (1988) 45–54. U.R. Kattner, W.J. Boettinger, J. Electron. Mater. 23 (1994) 603–610. Y. Xie, Z. Qiao, J. Phase Equilib. 17 (3) (1996) 208–217. C.S. Oh, J.H. Shim, B.J. Lee, D.N. Lee, J. Alloys Comp. 238 (1996) 155–166. F. Römermann, R. Blachnik, Z. Metallkd. 92 (4) (2001) 336–344. H. Flandorfer, C. Luef, U. Saeed, J. Non-Cryst. Solids 354 (2008) 2953–2972. T. Gomez-Acebo, CALPHAD 22 (2) (1998) 203–220. J.M. Fiorani, C. Naguet, J. Hertz, A. Bourkba, L. Bouirden, Z. Metallkd. 88 (9) (1997) 711–716. P. Anres, M. Alaoui-Elbelghiti, M. Gambino, J.P. Bros, Thermochim. Acta 346 (2000) 49. Y. Cui, X.J. Liu, I. Ohnuma, R. Kainuma, H. Ohtani, K. Ishida, J. Alloys Comp. 320 (2001) 234–241. Y. Xie, Z.Y. Qiao, A. Mikula, CALPHAD 25 (1) (2001) 3–10. N. Moelans, K.C. Hari Kumar, P. Wollants, J. Alloys Comp. 360 (2003) 98–106. B. Gather, P. Schroter, R. Blachnik, Z. Metallkd. 78 (1987) 280. X.J. Liu, Y. Inohana, Y. Takaku, I. Ohnuma, R. Kainuma, K. Ishida, Z. Moser, W. Gasior, J. Pstrus, J. Electron. Mater. 31 (11) (2002) 1139–1151. S. Karlhuber, K.L. Komarek, A. Mikula, Z. Metallkd. 8 (5) (1994) 307–311. M. Peng, Z. Qiao, A. Mikula, CALPHAD 22 (1998) 458. S. Knott, H. Flandorfer, A. Mikula, Z. Metallkd. 96 (2005) 1–7. G. Vassilev, V. Gandova, N. Milcheva, G. Wnuk, CALPHAD 43 (2013) 133–138. H. Flandorfer, F. Gehringer, E. Hayer, Thermochim. Acta 382 (2002) 77–87. A.T. Dinsdale, CALPHAD 15 (1991) 317–425. R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelly, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, International, Metals Park, OH, 1973.