RMZ - Materials and Geoenvironment, Vol. 57, No. 4, pp. 441-452, 2010
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Comparison between Sn-Ni-Zn liquid phase thermodynamic assessments performed by the CALPHAD method and by geometrical models
Primerjava med termodinamskim ovrednotenjem taline Sn-Ni-Zn z metodo CALPHAD in geometrijskimi modeli
V. GaNDOVA \ J. ROMANOWSKA2, G. VASSILEV 1 *
1 University of Plovdiv, Faculty of Chemistry, Plovdiv, Bulgaria 2Technical University of Rzeszow, Rzeszow, Poland
Corresponding author. E-mail: gpvassilev@gmail.com Received: May 25, 2010	Accepted: September 1, 2010
Abstract: Estimation of the thermodynamic properties of the Sn-Ni-Zn systems has been performed using the general solution model and by other geometric models. Description of the ternary liquid phase (Gibbs excess energy dependence on the temperature and the composition) was achieved using the available thermodynamic data of the constitutive binary systems (Ni-Zn, Sn-Zn, Sn-Ni). The validity of the geometric models was checked. The calculations have been performed in a wide temperature range (1000-2000 K). The calculated quantities were compared with the available literature data. Good agreement of the present assessment with thermodynamically optimized values of the system Sn-Ni-Zn (obtained by the CALPHAD approach) was observed.
Povzetek: Termodinamske lastnosti sistema Sn-Ni-Zn smo ovrednotili z uporabo splošnega modela raztopin in z drugimi geometrijskimi modeli. Ternarno talino (odvisnost presežne Gibbsove energije od temperature in kemijske sestave) smo opisali z uporabo dostopnih termodinamskih podatkov iz robnih binarnih sistemov (Ni-Sn, Sn-Zn in Sn-Ni). Preverili smo tudi veljavnost geometrijskih modelov. Izračune smo izvedli v širokem temperaturnem območju (1000-2000 K). Izračunane vrednosti smo primerjali s podatki iz literature. Rezultati tega ovrednotenja se dobro ujemajo s termodi-
Original scientific paper
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GANDOVA, V., ROMANOWSKA, J., VASSILEV, G.
namsko optimiranimi vrednostmi za sistem Sn-Ni-Zn, izračunanimi po metodi CALPHAD.
Key words: Sn-Ni-Zn system, liquid phase thermodynamics, general solution model, ternary interaction parameters Ključne besede: sistem Sn-Ni-Zn, termodinamika talin, splošni model raztopin, ternarni interakcijski parametri
Introduction
The Sn-Ni-Zn system is interesting as a potential lead-free solder material because of the termination of lead-containing solders industrial application is envisaged, due to the high lead toxicity. That is why the development of lead-free solders is a current task. These materials are expected to be designed on the bases of systems including low-melting elements like tin alloyed with zinc or/and bismuth. On the other side, nickel metallization often appears as intrinsic part of the electronic devices. Thus, investigations on a number of related solder/nickel systems and the corresponding properties were reported in the literature11, 2] but the thermodynamics of the system is still unknown.
The border-systems Ni-Sn[3-5] and Ni-Zn[6-10] are complex but they have been studied intensively. The binary system Sn-Zn presents a simple eutectic reaction.[11] These systems are included in the thermodynamic database developed by the European concerted action COST 531 and reliable thermodynamic optimizations are available for them.[12]
Nevertheless, there is no data about the thermochemical properties of the ternary liquid phase required for further thermodynamic optimization of the system Sn-Ni-Zn. Thus, the task of the present study is to apply different ways to assess the thermochemical properties of the ternary melt Sn-Ni-Zn.
Theoretical fundamentals of the
assessments
The so called "geometric models" give the possibility to predict the thermodynamic properties of a ternary phase (in this case - liquid) using data belonging to the respective binary border systems. In this work, assessments were made by means of the most common classic geometric models of Kohler,[13] Mug-gianu,[14] Toop[15] and Hillert[16] as well as by the newly-developed but prominent, general solution model (GSM) developed by Chou.[17, 18]
Hillert[16] classified the geometric models as symmetrical (e.g.[13, 14]) and asymmetrical (e.g.[15, 16]) while looking for a more universal approach to
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ternary properties prediction. Such a universal approach was recently developed by Chou[17, 18] and successfully employed in a variety of cases (e.g. ref. [19-22]). Nevertheless, a brief description of the techniques used shall be done below.
As usually, the molar excess Gibbs energy (AGE/(J mol1)) of the ternary liquid phase was chosen as a parameter which values had to be calculated by various models and compared. This quantity describes the contribution of the non-ideal mixing to the thermodynamic properties of a solution phase. The molar excess Gibbs energies values of all binary border-system (at a certain temperature and at specific compositions) are needed as starting points. These quantities were calculated by means of Thermocalc software package, using optimized parameters recently selected as result of the European concerted action for development of lead-free solders COST 531.[12]
In agreement with Redlich-Kister formalism, the composition dependence of the binary Gibbs molar excess energies ( AG^ ) is given by the expression:
a Gfj = Xi X j (A?j + 4 (Xi ~ X j) +
A}j tXi ~ X j)2 + - + A* CXi ~ X j)2)
(1)
Here, A0., A1., A2., are adjustable tem' y v y	J
perature dependent parameters belonging to the binary system " j"; X. and X
* J
indicate the mole fractions of the corresponding constituents. The Gibbs molar excess energy of a
27
ternary phase ( &G\23 ), consisting of elements 1, 2 and 3, is given by the expression:
AG123 = a + X2 X3 a gf3
+ X3XlAGf! + AG^3	(2)
where AG12, AGE23 and AG31 can be obtained as defined above (equation 1) and AGe123 is the contribution of the ternary non-ideal mixing. In the simplest case of a regular ternary solution it may be assessed by means of Equation (3):
AG^3 =^1X2^3^123 (3)
where A123 is a ternary interaction parameter that might be temperature and concentration dependent.
The most essential equations, associated to the geometrical models[1316] are only shown below only, because a detailed presentation would be out of the scope of this work. Thus, in a general case, a ternary system with constituents 1, 2 and 3 is considered where Xv X2 and X3 are the mole fractions of the respective components. The molar excess Gibbs energies of the ternary liq-
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GANDOVA, V., ROMANOWSKA, J., VASSILEV, G.
uid phase (at a specific composition, temperature and pressure,) are estimated by means of equations 4-7 according to the authors,[13-16] in the same order:
AGm = AG12 (1 - *3 )2 + AGf3 0 - ^ )2 + AGfl Q~x2)2	(4)
A^23 =-y AGf2 +-AGf3 +	(5)
(Xi +	+ f5 ) (X2 + f)(X3 + f)
-^-AG*
^23 = ^^2 +]ZYlAG!3 +^2 + X3;2AGf3	(6)
AGl=^AGn^AG^^AGl	(7)
1-X{	v23V32
In equations 4-7, the following symbols are represented: AGj23 - Gibbs molar excess energy of the ternary liquid phase; AG3.. - the respective values of the two-component liquid phases, where the subscript indexes indicate the considered binary system. The symbols v23 and v32 in equation (7) denote the mole fractions of the constituents 2 and 3 in the binary system 2-3. The values 1 - X1 and 1 - X3 are numerically equal in such a case.
Equation (3) will be used for introduction to the General solution model (GSM)
of CHou[17, 18]:
AGf23 = X\ X A X 3 /i 2 3	(8)
Here f123 is the ternary interaction coefficient, related to the Redlich-Kister ternary interaction parameters A..k (f123 = X1 • A0123 + X2 • A1123 + X3 • A2123) .
This parameter is assessed in the following way[17]:
fl23 = (2Šl2-V{ Ay(2Çn-l)X3 + 2( XI-X2)) + A\2} + (2Ç23-1)
(43«2Š23-l)Xi + 2(X2-X3)) + Al23} + (2š3l-l){All((2š3l-l)X2 + 2(X3-X\)) + A\x}	(9)
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Here are "similarity coefficients", that are defined by the quantity h called - "deviation sum of squares": = (10)
According to this model (GSM) the values of h are explicit functions of AG, and are easily calculated when the adjustable coefficients of the three binary end-systems are known.
Basic thermodynamic information on the constitutive subsystems, needed for the assessment, was taken from ref.[12] For the Ni-Sn liquid phase updated parameters were used.[24] Actually, the optimized Redlich-Kister parameters of each system (Table 1) are essentially needed. They are used for the calculation (equations 4-8) of the molar excess Gibbs
Table 1. Optimized parameters (A°., A1., A Sn[24], Ni-Zn[12] and Sn-Zn[12] systenis used
energies of the binary border-systems liquid phases. The following sequence of components was adopted for the calculations: Ni - 1, Sn - 2 and Zn - 3.
Results and Discussion
Calculations of the coefficients f 123 were done along three sections of the Ni-Sn-Zn system with molar Sn vs Zn ratios 1/3, 1/1 and 3/1 in the interval 1000-2000 K, at nickel molar fractions equal to 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1. In such a way a huge amount of information was obtained and used thereafter to derive the parameters A For this purpose programming of Excel was used. The results are shown in Table 2.
l2..) for the liquid binary phases of the Ni-in the present work; T/K - temperature.
System,	A0.. (T) J/mol	A1. (T) J/mol	A2. (T) J/mol
Ni-Sn (1-2)	-106102.87 + 197.9089 ■ T -21.9959 ■ T ■ LN(T)	-29342.17 + 52.5528 ■ T -6.46094 ■ T ■ LN(T)	+1582.3
Ni-Zn (1-3)	-50721.64 +7.34178 ■ T	+8436.3 +1.97211 ■ T	-25136.08 +11.79211 ■ T
Sn-Zn (2-3)	+19314.64 - 75.89949 ■ T +8.751396 ■ T ■ LN(T)	-5696.28 +4.20198 ■ T	+1037.22 +0.98362 ■ T
Table 2. Ternary interaction parameters, Avjk, for the Sn-Ni-Zn liquid phase obtained from the f 123 coefficients. T/K - temperature.
System, iJk	A0ijk (T J/mol	A1ijkT J/mol	A2ijkT J/mol
Sn-Ni-Zn	-884.2 + 6.5534 ■ T	45415 - 18.16 ■ T	-28292.6 + 17.82 ■ T
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GANDOVA, V., ROMANOWSKA, J., VASSILEV, G.
As already mentioned the binary integral Gibbs excess energies ought to be obtained initially. This was done by the Thermocalc software package, calculating binary activity values (referred to the liquid phases of the pure elements) at the pertinent points.
The ternary integral molar Gibbs excess energies assessed by the geometrical methods are graphically compared to those obtained by Thermocalc, using the optimized adjustable parameters of the border-systems only (Table 1). Sections with constant molar ratios between two of the components are plotted.
Results from a section with constant molar Sn/Zn equal to 1/3, at 1800 K are plotted in Figure 1. As one can see the curves 2 and 6 from one side and 1, 4 and 5 from the other side are grouped
together, while the CALPHAD-type calculated values (curve 3) are situated between both groups. Surely, one has to bear in mind that curve 3 contains values assessed by binary parameters only. The
asymmetrical methods (curves 4 and 5)
p
give practically equal AG 123 values while the quantities obtained by symmetrical methods (curves 1 and 6) differ significantly between each other. It should be noted that curve 6 (Muggiani model) is situated below all other curves at both other Sn/Zn ratios_(1/1 and 3/1).
Figure 2 represents ternary integral molar Gibbs excess energies assessed along a molar Ni/Zn ratio equal to 1/3, at 1800 K. In this case, the values assessed by symmetrical methods (curves 1 and 6) are quite similar and are accompanied by the CALPHAD-type calculated quanti-
Figure 1. Molar Gibbs excess energies (AGex Liq J/mol) of the liquid phase, along a section with constant molar Sn/Zn ratio equal to 1/3, at 1800 K calculated in this work according to various techniques: 1 - up to Kohler,[13] 2 - GSM,[34] 3 - CALPHAD (binary parameters only), 4 - Toop,[15] 5 - Hillert[16] and 6 - Muggianu.[14]
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OA	0.0
Mole fraction Sn
Figure 2. Molar Gibbs excess energies (AGex Liq, J/mol) of the liquid phase, along a section with constant molar Ni/Zn ratio equal to 1/3, at 1800 K calculated in this work according to various techniques: 1 - up to Kohler,[13] 2 - GSM,[34] 3 - CALPHAD (binary parameters only), 4 - Toop,[15] 5 - Hillert[16] and 6 - Muggianu.[14]
ties (curve). The same is valid for the values calculated by both asymmetrical methods (curves 4 and 5). The GSM-assessed integral molar Gibbs excess energies (curve 2) deviate from all others. Similar disposition of the considered curves is observed at the sections along molar Ni/Zn ratios equal to 1/1 and 3/1.
It can be seen in Figure 3 ( AG^ values along Sn/Ni molar ratio equal to 1/3, at 1800 K, are plotted) that the curves 1-3, from one side and 4-6, from the other side, are rather close to each another. Thus, the type of the method (symmetric or asymmetric) does not play a decisive role regarding the values of the calculated AG^ •
The ^^123 values assessed in various ways along the sections with Sn/
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Ni molar ratios equal to 1/1 and 3/1 are roughly similar. The results for the ratio 3/1 are shown in Figure 4 in order to illustrate the shape of the curves.
In order to represent ^^123 temperature dependence the values of the integral ternary molar Gibbs excess energies are plotted in Figures 5-7. The latter were calculated by GSM (by equations 9 and 10, using the parameters shown in Table 1) in the temperature range 1000-2000 K and along sections with Sn/Zn, Ni/Zn and Sn/Ni molar ratios equal to 1/1, respectively. Negative deviations from the Raoult's low are observed in general while in the regions rich of tin and zinc feeble positive AG^ are observed only.
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GANDOVA, V., ROMANOWSKA, J., VASSILEV, G.
Figure 3. Molar Gibbs excess energies (AGex Liq, J/mol) of the liquid phase, along a section with constant molar Sn/Ni ratio equal to 1/3, at 1800 K calculated in this work according to various techniques: 1 - up to Kohler,[13] 2 - GSM,[34] 3 - CALPHAD (binary parameters only), 4 - Toop,[15] 5 - Hillert[16] and 6 - Muggianu.[14]
Figure 4. Molar Gibbs excess energies (AGex Liq, J/mol) of the liquid phase, along a section with constant molar Sn/Ni ratio equal to 3/1, at 1800 K calculated in this work according to various techniques: 1 - up to Kohler,[13] 2 - GSM,[34] 3 - CALPHAD (binary parameters only), 4 - Toop,[15] 5 - Hillert[16] and 6 - Muggianu.[14]
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Figure 5. Calculated by GSM values of the integral ternary molar Gibbs excess energies in the temperature range 1000-2000 K. Section with Sn/Zn ratio equal to 1/1. AGex Liq, J/ mol - molar Gibbs excess energy of the ternary liquid phase; xNi- nickel mole fraction; T/K - temperature.
Figure 6. Calculated by GSM values of the integral ternary molar Gibbs excess energies in the temperature range 1000-2000 K. Section with Ni/Zn ratio equal to 1/1. AGex Liq, J/ mol - molar Gibbs excess energy of the ternary liquid phase; xgn- tin mole fraction; T/K - temperature.
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GAndova, V., ROMANOWSKA, J., VASSILEV, G.
Figure 7. Calculated by GSM values of the integral ternary molar Gibbs excess energies in the temperature range 1000-2000 K. Section with Sn/Ni ratio equal to 1/1. AGex Liq, J/ mol - molar Gibbs excess energy of the ternary liquid phase; xZn- zinc mole fraction; T/K - temperature.
Conclusions
Some thermodynamic properties of the Sn-Ni-Zn liquid phase were predicted using a general solution model developed by Chou, two symmetrical and two asymmetrical models. Redlich-Kister ternary interaction parameters of the liquid phase were assessed.
The values of the ternary liquid phase molar Gibbs excess energies assessed by geometric models were compared to those calculated by the CALPHAD method using binary optimized parameters only. Good mutual agreement was found indicating that the interaction parameters for the ternary system would have small values.
Acknowledgments
This work is related to the European concerted action COST MP 0602 and is financed by the University of Plovdiv (NPD) under contract No. RS09-HF-023.
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