Calculation of thermodynamic properties for ternary Ag-Cu-Sn system
Saša Marjanovic 1, Dragan Manasijevic 1, Dragana Živkovic 1, Dragoslav Guskovic 1,
Duško Minic2
'University of Belgrade, Technical Faculty, Dept. of Metallurgy, VJ 12, 19210 Bor, Serbia;
E-mail: smarjanovic@tf.bor.ac.yu 2University of Pristina, Faculty of Technical Sciences, 38220 Kosovska Mitrovica, Serbia
Received: January 13, 2009	Accepted: February 17, 2009
Abstract: Results of thermodynamic properties calculations for the liquid alloys in ternary Ag-Cu-Sn system are presented in this paper. The general solution model has been used for the thermodynamic prediction in the sections from each component corner, with the molar ratio of the other two components 1:9, 3:7, 1:1, 7:3, 9:1, for which characteristic thermodynamic quantities have been obtained at temperature 1473 K.
Key words: Ag-Cu-Sn alloys, thermodynamics, general solution model
Introduction
The Ag-Cu-Sn system is fundamental to the development of technology of lead-free solder alloys. Recent legislations in many countries to eliminate the use of lead containing solder alloys have created renewed interest in this system, especially in the Sn rich region.
This system has rather already been investigated. Thus, Yen and Chen[1] have determined phase equilibria of the Ag-Sn-Cu ternary system experimentally as well as using the calculation of phase diagram (CALPHAD) method. Ohnuma et al.[2] have presented the phase equilibria and the related thermodynamic properties of the Sn-Ag-Cu alloys using a thermodynamic
database for micro-soldering alloys that consists of the elements Pb, Bi, Sn, Sb, Cu, Ag, Zn and In. Hirose et al.[3] have investigated joint strength and interfacial microstructure between Sn-Ag-Cu and Sn-Zn-Bi solders and Cu substrate. Dutkiewicz et al.[4] have investigated rapid quenching and mechanical alloying of eutectic Ag-Cu-Sn alloys. He and Ding[5] have investigated Ag-Cu-Sn brazing filler metals. Also, Moon et al.[6] have investigated experimentally and made thermodynamic assessment of Sn-Ag-Cu solder alloys.
The latest thermodynamic assessment of Ag-Cu-Sn ternary system is work of Gisby and Dinsdale [7] carried out prior the COST 531 Action[8] and included in COST 531 Database for Lead Free Solders[9] and
in COST 531 Atlas of Phase Diagrams for	In this paper, in order to investigate ther-
Lead-Free Soldering[10]. The calculated	modynamic behavior of liquid Ag-Cu-Sn binary systems and liquidus projection of alloys and its relationship with phase struc-
ternary Ag-Cu-Sn system according to	ture of solidified alloys, several integral
Reference[10] are shown in Figure 1. The	and partial thermodynamic functions were
phase diagram of the Ag-Cu binary sys-	calculated using Chou's general solution
tem is rather simple without intermediate	model. Obtained results were discussed in
phases and the phase diagrams of the Ag-	connection with a mutual reactivity of the
Sn and Cu-Sn are complex with appear-	components in investigated ternary sys-
ance of many intermediate phases.	tem.
Figure 1. Phase diagrams of the boundary binary systems, and the liquidus projection of the ternary Ag-Cu-Sn system[10]
Theoretical fundamentals
There are several traditional models to extrapolate thermodynamic properties of the ternary system based on the three constitutive binary systems, which are classified, according to Hillert[11], into two categories: symmetrical (Kohler[12], Muggianu [13]) and asymmetrical (Toop [14], Hillert [11]).
The use of a symmetrical model when an asymmetrical model is more appropriate can often give rise to errors. Categorization of the investigated ternary system in the one of these two categories is, in some cases and in the lacking of the adequate experimental data, uncertain task. Also, a different choice of an arrangement of the three components to the three apexes of triangle in the case of the asymmetric model application will lead to a different result of the ternary Gibbs energy of mixing. From this reasons Chou [15,16] proposed a new model, based on the "similarity coefficient concept", which advantage is that its application does not require predetermination if a system is symmetrical or not, neither choice of the symmetric and asymmetric components in the particular ternary system. The correctness of this model has already been confirmed in some practical examples[17-19]. Therefore this model is applied for the calculation of the thermodynamic properties of the liquid Ag-Cu-Sn ternary system.
The basic equation of general solution model developed by Chou is given as follows (in detail see References[15,16] ):
Age = x1x2 (Ao12 + A112 (x1-x2) + A212 (x1-x2)2) +
+ x2x3 (A°23 + A123 (x2-x3) + A223 (x2-x3)2) + x3x1 (A°3i + A131 (x3-x1) + A23! (x3-x1)2) + + fX1X2X3	(1)
where AG is an integral excess Gibbs energy for a ternary system, x1 x2 x3 are the mole fractions of a ternary alloy, Aoij, A1ij, A2ij are regular-solution type parameters for binary system "ij" and can be temperature dependent.
The function f is the ternary interaction coefficient expressed by:
f = (2^12 -1){A212 ((2^12 -1)X3 + 2(X1-X2)) +
+ A112} + ^23 -1){A223 (^23 ^ +
+ 2(X2-X3)) + A123} + (2^31 -1){A231 ((2^31 -
-1)X2 + 2(X3-X1)) + A131}	(2)
where ^ are the similarity coefficients defined by ni called the deviation sum of squares:
^n/H+np	(3)
where are:
and
(5)
Results and discussion
The thermodynamic calculation were performed using general solution model, in the sections from each component corner with the molar ratio of the other two components 1:9, 3:7, 1:1, 7:3, 9:1 at chosen temperature 1473 K. This temperature is appropriate for analysis of atomic interaction in liquid phase because it is not too high. The starting data values of Redlich-Kister parameters of the liquid phases of the binary systems Ag-Cu, Ag-Sn, and Cu-Sn are shown in Table 1.
For the calculation of integral excess Gibbs energy using Chou's model we arbitrary adopted following settings of components: Ag-component 1, Cu-component 2 and Sn-component 3. Therefore the Redlich-Kister parameters (named with L;. in Table 1) for the Ag(1) - Cu(2) and Cu(2 ) - Sn(3) binary systems are identical to regular-solution type parameters appearing in Chou's model (named with A. in Eqs. 1,2). Only for the second parameter in the Sn(3) - Ag(1) binary system stands following relation A. = -L. Calculated regular-solution type parameters for constitutive binaries, deviation sum of squares and similarity coefficients for the ternary Ag-Cu-Sn system at 1473 K are presented in Table 2.
Using the values from Table 1 and Equation 1 AGe functions for boundary binary systems and chosen ternary sections at 1473 K were calculated and shown in Figure 2.
Table 1. The Redlich-Kister parameters for boundary binary systems
Parameter	Ag-Cu[20-21]	Ag-Sn[22]	Cu-Sn[23]
L0. ■i	+ 17384.37 - 4.46438 T	- 5146.7 - 5.0103T	- 9002.8 - 5.8381 T
L1.. ■i	+ 1660.74 - 2.31516T	- 15799.3 + 3.3208 T	- 20100.4 + 3.6366 T
L2. ■i	-	- 6687.5	- 10528.4
Table 2. Regular-solution type parameters for Ag-Cu, Cu-Sn and Sn-Ag binaries, deviation sum of squares and similarity coefficients for the ternary Ag-Cu-Sn system at 1473 K (Ag-Cu-Sn set in 1-2-3 order).
A AgCu	A AgCu	A AgCu	ni	^Ag-Cu
10808.34	1749.491	0	2.01E+07	0.391709
A0 CuSn	A 1 CuSn	A2 CuSn	nii	^Cu-Sn
— 17602.3	— 14743.29	- 10528.4	3.12E + 07	0.881417
A SnAg	A SnAg	A SnAg	niii	^Sn-Ag
- 12526.9	10907.76	- 6687.5	4200970	0.172818
E
2DOO-	Ag-C" . * * ■ > SI , .	• *
snn.	*	* *
a-	• * . " •	
-lOffl--7TO-	11 . - T	
	. * : » - * i »	# 1.9 4 ---4 *
J™.	, *	Ag-Sn
■ion.		
a)
-3 e

b)
	
■ ' ^------ *	
	jt •
"^•g^rT^ 1=1 , jr	-* 9
	
	Cu-5n
c)
In Figure 2 it can be observed that Cu-Ag binary system has positive values AG2 in whole concentration range, while the other two constitutive binary systems have negative values AG2. According to this, chemical interaction between atoms Sn on one side and atoms Cu and Ag on the other side is much stronger than chemical interaction between atoms Cu and Ag. This causes that in solid state Ag and Cu do not make any new intermediate phases while Sn with both Cu and Ag forms a series of intermediate phases. This tendency is held in ternary system. According to the liqui-dus projection of the Ag-Cu-Sn system, shown in Figure 1, for the alloys with low concentration of Sn, primary crystallization phases are solid solutions based on Ag and Cu and for alloys with moderately and high concentration of Sn primary crystallization phases are intermediate phases based on Sn.
According to calculated dependence of Gxs of composition, and using equations (4) and (5), partial thermodynamic quantities have been obtained.
Gxsi = Gxs + (1 - xi) (3Gxs/3xi) Gxsi = RT ln(a /x)
(6) (7)
Figure 2. Dependence of AGE on molar frac-	^ .	,, .	. . . „...
fv-f u-	+ a u	Dependence of the partial molar Gibbs
tion of Xi for three binary systems and chosen ^	^
ternary sections at 1473 K (a - Ag-corner, b -	free energies on c°mp°sition of each com-
Cu-corner, c - Sn-corner)	ponent at 1473K is shown in Figure 3.
6000 0
-5000 ■10000 -15000 -20000 -25000 -30000 -35000
c)
xsn
	Sn-Ag
	
■	7:3
*	
	3:7 1:9 Sn-Cu
	
b)
Figure 3. Dependence Gxsi on composition of components for all observed sections in Cu-Ag-Sn system at 1473 K(a - Ag-corner, b - 100 Cu-corner, c - Sn-corner)
c)
Further calculation involves determining
the dependence of activity of components	Figure 4. Iso-activity lines for Cu (a), Ag (b),
of composition in the observed sections of	and Sn (c) in ternary Cu-Ag-Sn system at
the ternary Cu-Ag-Sn system.	1473 K
The calculated activities of the components in Cu-Ag-Sn system at 1473K indicate that activities of Ag and Cu decrease rapidly with increase of Sn content in ternary alloys. Minimum of thermodynamic activity Ag and Cu achieve in boundary Ag-Sn and Cu-Sn systems which is in agreement with their strong chemical affinity toward Sn. Variation of Ag and Cu concentration in ternary Ag-Cu-Sn alloys has much less influence on Sn activity.
son with future experimental results in order to determine the deviation and to define ternary interaction parameters.
Acknowledgement
The authors are grateful to the Ministry of Science of the Republic of Serbia (Project N0142043) for financial support.
References
Iso-activity lines for Cu, Ag, and Sn at m 1473 K that illustrate previously mentioned facts are shown in Figure 4.
[2]
Conclusions
Thermodynamic analysis of the liquid Cu- [3] Ag-Sn alloys has been carried out with geometrical Chou's general solution model for predicting the thermodynamic quantities of ternary alloys according to known [4] thermodynamic quantities of the constituting binary systems. Integral excess Gibbs free energies for fifteen distinguished sections at 1473 K have been calculated. Fur- [5] ther calculation has involved obtaining of the partial molar Gibbs free energies, and [6] diagrams of iso-activity lines for all three components have been constructed. It has been determined that thermodynam-ic properties of the constituting binary systems define thermodynamic behavior of [7] the ternary system alloys, and that chemical affinities between the elements in bi- [8] nary systems remain in ternary alloys, as well.
[9]
Presented results can be used for compari-
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