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Experimental study and thermodynamic calculation of Bi–Cu–Sb system phase equilibria
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Intermetallics 16 (2008) 107e112 www.elsevier.com/locate/intermet
Experimental study and thermodynamic calculation of BieCueSb system phase equilibria D. Manasijevic´ a,*, D. Minic´ b, D. Zˇivkovic´ a, D. Rajnovic´ c a University of Belgrade, Technical Faculty, VJ 12, 19210 Bor, Serbia University of Pristina, Faculty of Technical Science, 38220 Kosovska Mitrovica, Serbia c University of Novi Sad, Faculty of Technical Sciences, Trg D. Obradovic´a 6, 21000 Novi Sad, Serbia b
Received 5 January 2007; received in revised form 5 July 2007; accepted 15 August 2007 Available online 24 October 2007
Abstract Phase equilibria in the BieCueSb ternary system have been studied experimentally and calculated by the CALPHAD method. Three calculated vertical sections from bismuth corner with molar ratio of copper and antimony equal to 7/3, 1/1 and 3/7 and one vertical section from antimony corner with molar ratio of copper and bismuth equal to 1/1 were compared with the DTA results from this work. Calculated isothermal section at 400 C was compared with the results of SEM/EDX analysis from the present study. Reasonable agreement between calculations and experimental data was observed in all cases. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Ternary alloy systems; B. Phase diagrams; E. Phase diagram, prediction
1. Introduction The elements Bi, Cu and Sb are important for the design of microsoldering and substrate materials. Therefore, knowledge of the phase equilibria in the BieCueSb ternary system is desirable for the development of lead-free solder alloys. Thermodynamic modeling of phase equilibria in perspective systems represents first necessary step for development of new lead-free soldering materials. For this purpose, in the frame of COST 531 action [1] and SGTE, thermodynamic database based on recent version 4.4 SGTE [2] values of Gibbs energies for a pure element was developed [3]. It contains the data for carefully tested binary phase diagrams, suitable for prediction of phase equlibrium in multicomponent systems. In this paper, the BieCueSb ternary system is investigated via experiment and thermodynamic binary-based prediction according to CALPHAD technique. Calculated vertical sections
* Corresponding author. Tel./fax: þ381 30 424 547. E-mail address: [email protected] (D. Manasijevic´). 0966-9795/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2007.08.005
from bismuth and antimony corners and isothermal section at 400 C were compared with experimental results based on DTA and SEM/EDX from the present study. 2. Experimental procedure All samples were prepared from Bi, Cu and Sb shots of 99.99% purity. The samples, having masses approximately 5 g, were prepared in an induction furnace under high purity argon. As Sb is easy to volatilize, before melting an extra amount of Sb (about 3e5 wt.%) was added to compensate the weight loss. After melting, the samples were sealed in evacuated quartz tubes for homogenization heat treatment. The samples were annealed at 400 C for 200 h. After annealing, samples prepared for DTA measurements were gradually cooled down in order to obtain stable equilibrium at room temperature. Samples prepared for SEM/EDX investigation were quenched into ice water. The equilibrium compositions of phases were determined using JEOL JSM-6460 scanning electron microscope with accelerating voltage 20 kV and EDX analyzer.
108
Table 1 Optimized thermodynamic parameters for constitutive binaries used in this study Ref.
G(LIQUID,BI;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ þ3428.29 þ 107.782416*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 5.9549E 19*T7 (298.14 < T < 544.54) þ41544.282 414.460769*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3616168*T(1) (544.54 < T < 800.00) þ290.595 þ 161.738553*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 (800.00 < T < 1200.00) þ3754.947 þ 103.961021*T 27.196*T*LN(T ) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
G(LIQUID,CU;0) H298(FCC_A1, CU;0)¼ þ5194.277 þ 120.973331*T 24.112392*T*LN(T ) 0.00265684*T2 þ 1.29223E 07*T3 þ 52478*T(1) 5.8489E 21*T7 (298.14 < T < 1357.77) 46.545 þ 173.881484*T 31.38*T*LN(T ) (1357.77 < T < 3200.00)
[2,3] [2,3]
G(LIQUID,SB;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ þ10579.47 þ 134.231525*T 30.5130752*T*LN(T ) þ 0.007748768*T2 3.003415E 06*T3 þ 100625*T(1) 1.74847E 20*T7 (298.14 < T < 903.78) þ8175.359 þ 147.455986*T 31.38*T*LN(T ) (903.78 < T < 2000.00) L(LIQUID,BI,CU;0) ¼ þ 20,747.5 5.85*T L(LIQUID,BI,CU;1) ¼ 4925 þ 2.55*T L(LIQUID,BI,CU;2) ¼ þ4387.5 2.3*T L(LIQUID,BI,SB;0) ¼ þ2230 þ 0.06*T L(LIQUID,CU,SB;0) ¼ 16,154.82 þ 23.99549*T 4.0284*T*LN(T ) L(LIQUID,CU,SB;1) ¼ 35,130.8 þ 50.3301*T 5.2316*T*LN(T ) L(LIQUID,CU,SB;2) ¼ 29,263.28 þ 15.3192*T L(LIQUID,CU,SB;3) ¼ 2300.89 L(LIQUID,CU,SB;4) ¼ 8873.94
[2,3] [2,3] [3,4] [3,4] [3,4] [3,5] [3,6] [3,6] [3,6] [3,6] [3,6]
FCC_A1 2 SUBLATTICES, SITES 1:1 CONSTITUENTS: BI,CU,SB: VA G(FCC_A1,BI:VA;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ þ2082.224 þ 115.918925*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 (298.14 < T < 544.54) þ40108.022 406.150351*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3616168*T(1) þ 1.66145E þ 25*T(9) (544.54 < T < 800.00) 1145.664 þ 170.048971*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 þ 1.66145E þ 25*T(9) (800.00 < T < 1200.00) þ2318.688 þ 112.27144*T 27.196*T*LN(T ) þ 1.66145E þ 25*T(9) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
G(FCC_A1, CU:VA;0) H298(FCC_A1, CU;0)¼ 7770.458 þ 130.485235*T 24.112392*T*LN(T ) 0.00265684*T2 þ 1.29223E07*T3 þ 52478*T(1) (298.14 < T < 1357.77) 13542.026 þ 183.803828*T 31.38*T*LN(T ) þ 3.64167E þ 29*T(9) (1357.77 < T < 3200.00)
[2,3] [2,3]
G(FCC_A1, SB:VA;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ þ10631.142 þ 142.454689*T 30.5130752*T*LN(T ) þ 0.007748768*T2 3.003415E 06*T3 þ 100625*T(1) (298.14 < T < 903.78) þ 8135.17 þ 155.785872*T 31.38*T*LN(T ) þ 1.616849E þ 27*T(9) (903.78 < T < 2000.00) L(FCC_A1,BI,CU:VA;0) ¼ þ50*T L(FCC_A1,BI,SB:VA;0) ¼ þ10,150 6.3*T L(FCC_A1,CU,SB:VA;0) ¼ 8534 10.44293*T
[2,3] [2,3] [3] [3] [3,6]
BCC_A2 2 SUBLATTICES, SITES 1:3 CONSTITUENTS: BI,CU,SB:VA G(BCC_A2,BI:VA;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ þ3479.224 þ 114.518925*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 (298.14 < T < 544.54) þ41505.022 407.550351*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3,616,168*T(1) þ 1.66145E þ 25*T(9) (544.54 < T < 800.00) þ251.336 þ 168.648971*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 þ 1.66145E þ 25*T(9) (800.00 < T < 1200.00) þ3715.688 þ 110.87144*T 27.196*T*LN(T ) þ 1.66145E þ 25*T(9) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
LIQUID CONSTITUENTS: BI,CU,SB
[2,3] [2,3]
G(BCC_A2, SB:VA;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ þ10631.142 þ 141.054689*T 30.5130752*T*LN(T ) þ 0.007748768*T**2 3.003415E 06*T3 þ 100625*T(1) (298.14 < T < 903.78) þ8135.17 þ 154.385872*T 31.38*T*LN(T ) þ 1.616849E þ 27*T(9) (903.78 < T < 2000.00) L(BCC_A2,BI,CU:VA;0) ¼ þ50*T L(BCC_A2,BI,SB:VA;0) ¼ þ10,150 6.3*T L(BCC_A2,CU,SB:VA;0) ¼ þ50,092.341 41.561183*T L(BCC_A2,CU,SB:VA;1) ¼ 331,192.835 þ 110.62385*T L(BCC_A2,CU,SB:VA;2) ¼ þ301,571.206 þ 15*T L(BCC_A2,CU,SB:VA;3) ¼ 984.45639 77.2521*T L(BCC_A2,CU,SB:VA;4) ¼ 90*T
[2,3] [2,3] [3] [3] [3,6] [3,6] [3,6] [3,6] [3,6]
RHOMBOHEDRAL_A7 CONSTITUENTS: BI,SB G(RHOMBOHEDRAL_A7,BI;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ 7817.776 þ 128.418925*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 (298.14 < T < 544.54) þ30,208.022 393.650351*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3,616,168*T(1) þ 1.66145E þ 25*T(9)(544.54 < T < 800.00) 11,045.664 þ 182.548971*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 þ 1.66145E þ 25*T(9) (800.00 < T < 1200.00) 7581.312 þ 124.77144*T 27.196*T*LN(T ) þ 1.66145E þ 25*T(9) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
G(RHOMBOHEDRAL_A7, SB;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ 9242.858 þ 156.154689*T 30.5130752*T*LN(T ) þ 0.007748768*T2 3.003415E 06*T3 þ 100625*T(1) (298.14 < T < 903.78) 11738.83 þ 169.485872*T 31.38*T*LN(T ) þ 1.616849E þ 27*T(9) (903.78 < T < 2000.00) L(RHOMBOHEDRAL_A7,BI,SB;0) ¼ þ 10,150 6.3*T L(RHOMBOHEDRAL_A7,BI,SB;1) ¼ 150
[2,3] [2,3] [3,5] [3,5]
CUSB_ZETA 2 SUBLATTICES, SITES 0.77:0.23 CONSTITUENTS: CU:SB G(CUSB_ZETA,CU:SB;0) 0.77H298(FCC_A1,CU;0) 0.23H298(RHOMBOHEDRAL_A7,SB;0) ¼ 4936.60.94*T þ 0.77*GHSERCU þ 0.23*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_GAMMA 2 SUBLATTICES, SITES 0.85:0.15 CONSTITUENTS: CU:SB G(CUSB_GAMMA,CU:SB;0) 0.85H298(FCC_A1,CU;0) 0.15H298(RHOMBOHEDRAL_A7,SB;0) ¼ 26801.8*T þ 0.85*GHSERCU þ 0.15*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_ETA 2 SUBLATTICES, SITES 0.67:0.33 CONSTITUENTS: CU:SB G(CUSB_ETA,CU:SB;0) 0.67H298(FCC_A1,CU;0) 0.33H298(RHOMBOHEDRAL_A7,SB;0) ¼ 4350.7723.888*T þ 0.67*GHSERCU þ 0.33*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_EPSILON 2 SUBLATTICES, SITES 0.75:0.25 CONSTITUENTS: CU:SB G(CUSB_EPSILON,CU:SB;0) 0.75H298(FCC_A1,CU;0) 0.25H298(RHOMBOHEDRAL_A7,SB;0) ¼ 4718 1.69*T þ 0.75*GHSERCU þ 0.25*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_DELTA 2 SUBLATTICES, SITES 0.8:0.2 CONSTITUENTS: CU:SB G(CUSB_DELTA,CU:SB;0) 0.8H298(FCC_A1,CU;0) 0.2H298(RHOMBOHEDRAL_A7,SB;0) ¼ 5142 þ 0.8*GHSERCU þ 0.2*GHSERSB (298.14 < T < 3000.00)
[3,6]
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
G(BCC_A2, CU:VA;0) H298(FCC_A1,CU;0)¼ 3753.458 þ 129.230235*T 24.112392*T*LN(T )0.00265684*T2 þ 1.29223E07*T3 þ 52478*T(1) (298.14 < T < 1357.77) 9525.026 þ 182.548828*T 31.38*T*LN(T ) þ 3.64167E þ 29*T(9) (1357.77 < T < 3200.00)
109
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
110
Table 2 DTA results for the investigated alloys of the BieCueSb ternary system Sample composition (at.%)
Thermal effect ( C) Liquidus temperature
Other peak temperature
Cu:Sb ¼ 7:3 Bi10Cu63Sb27 Bi20Cu56Sb24 Bi30Cu49Sb21 Bi40Cu42Sb18 Bi50Cu35Sb15 Bi60Cu28Sb12 Bi70Cu21Sb9 Bi80Cu14Sb6 Bi95Cu3.5Sb1.5
649 642 650 654 657 662 655 646 494
269, 278, 284, 282, 294, 283,
406, 414, 406, 423, 425, 422, 268, 273,
555 525 521 512 532 513 485 426 286
Cu:Sb ¼ 1:1 Bi10Cu45Sb45 Bi20Cu40Sb40 Bi30Cu35Sb35 Bi40Cu30Sb30 Bi50Cu25Sb25 Bi60Cu20Sb20 Bi70Cu15Sb15 Bi80Cu10Sb10 Bi90Cu5Sb5
582 573 596 621 641 647 658 646 581
419, 353, 347, 415, 333, 316, 306, 298, 282, 280,
492 451 569 574 561 547 539 520 488
Cu:Sb ¼ 3:7 Bi10Cu27Sb63 Bi20Cu24Sb56 Bi30Cu21Sb49 Bi40Cu18Sb42 Bi50Cu15Sb35 Bi60Cu12Sb28 Bi70Cu9Sb21 Bi80Cu6Sb14 Bi90Cu3Sb7
507 552 538 561 572 564 555 524 492
e 394, 363, 312, 299, 295,
478 463 437 361 336 302 294 288
Bi:Cu ¼ 1:1 Bi45Cu45Sb10 Bi40Cu40Sb20 Bi35Cu35Sb30 Bi30Cu30Sb40 Bi25Cu25Sb50 Bi20Cu20Sb60 Bi15Cu15Sb70 Bi10Cu10Sb80 Bi5Cu5Sb90
632 657 629 586 548 506 515 565 593
270, 383, 472, 583 279, 424, 492 293, 379, 564 303, 454 384, 497 e 452 522 513
DTA measurements were carried out with the Derivatograph (MOM Budapest) apparatus under following conditions: argon atmosphere, heating rate 5 C/min using sintered Al2O3 as the reference specimen. 3. Thermodynamic modeling The pure solid elements in their stable form at 298.15 K and under the pressure of 1 bar were chosen as the reference state for the systems (SER). The Version 4.4 of the SGTE Unary Database (Scientific Group Thermodata Europe) of phase stabilities for stable and metastable states of pure elements [2] was used. Thermodynamic data for the BieCu system were taken from Ref. [4], for the BieSb system were published in
Ref. [5], and thermodynamic data for the system CueSb were taken from Ref. [6]. All these data are included in the COST 531 Database for Lead-Free Solders [3]. The following phases from constitutive binary subsystems were considered for thermodynamic binary-based prediction: liquid phase, the Cu-based fcc solution (denoted as FCC_A1), Sb and Bi rich solid solution (denoted as RHOMBOHEDRAL_A7), b phase with bcc structure (denoted as BCC_A2 phase), z (Cu10Sb3), g (Cu17Sb3), h (Cu2Sb), 3 (Cu3Sb), and d (Cu4Sb) intermediate phases from CueSb binary systems with very narrow concentration ranges of existence denoted as: CUSB_ZETA, CUSB_GAMMA, CUSB_ETA, CUSB_ EPSILON, and CUSB_DELTA, respectively. The Gibbs energies of the liquid, fcc, bcc and rhombo phases are described by a substitution solution model and a RedlicheKister formalism. All of the compounds were treated as stoichiometric compounds. Phase diagram of the BieCueSb ternary system was calculated using only optimized thermodynamic parameters for constitutive binary systems. No further thermodynamic optimization was done in the present work. Optimized thermodynamic parameters of constitutive binary systems used for calculation are shown in Table 1. 4. Results and discussion 4.1. Isopleths (vertical sections) Four characteristic isopleths of the BieCueSb ternary system were experimentally investigated by DTA. The analysis of DTA measurements was performed on DTA curves obtained during the heating of samples. Temperatures of phase transitions were read using software delivered with the instrument. The results are shown in Table 2. Mutual comparison between DTA results and calculated phase diagrams is presented in Fig. 1. It can be seen that there is a reasonable agreement between DTA results from this work and calculated phase diagrams for all investigated isopleths. Calculated liquidus temperatures are confirmed quite well by DTA measurements. Calculated vertical section with molar ratio Cu:Sb ¼ 7:3 includes three primary crystallization areas (liquid þ BCC_A2; liquid þ CUSB_DELTA and very narrow primary crystallization region of liquid þ Rhombo (Bi)), vertical section with molar ratio Cu:Sb ¼ 1:1 includes four primary crystallization areas (liquid þ BCC_A2; liquid þ CUSB_DELTA; liquid þ CUSB_ETA and narrow liquid þ Rhombo (Bi)), vertical section with molar ratio Cu:Sb ¼ 3:7 includes three primary crystallization areas (liquid þ BCC_A2; liquid þ Rhombo; liquid þ CUSB_ETA) and vertical section from antimony corner with molar ratio Bi:Cu ¼ 1:1 includes four primary crystallization areas (liquid þ FCC_A1, liquid þ BCC_A2; liquid þ Rhombo; liquid þ CUSB_ETA). 4.2. Isothermal section at 400 C The SEM (scanning electron microscope) with EDX (energy dispersive X-ray) analyzer was used for determination
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
111
Fig. 1. .Calculated vertical sections of the BieCueSb ternary system with DTA results from the present study: (a) Cu:Sb ¼ 7:3, (b) Cu:Sb ¼ 1:1, (c) Cu:Sb ¼ 3:7 and (d) Bi:Cu ¼ 1:1.
of composition of coexisting phases at 400 C. Two quenched samples with predicted three-phase structure and one sample with predicted two-phase structure were analyzed. All results from SEM analysis are given in the Table 3. Comparison of calculated phase diagram of the BieCueSb ternary system at 400 C with experimental results from this work is shown in Fig. 2. Predicted phase structure was experimentally confirmed for all three analyzed samples. Experimentally determined
compositions of CUSB_ETA and CUSB_DELTA phases are in good agreement with calculated phase diagram as well as determined solubility of antimony in the fcc copper-rich phase. Former liquid phase had very inhomogeneous structure and strong dispersion of obtained results by EDX point analysis with large experimental error (up to 4 at.%) were noticed. These large standard errors were probably caused by decomposition of equilibrated liquid during quick cooling and solidification.
Table 3 Results of the SEM-EDX analysis at 400 C Overall experimental composition (at.%)
Theoretically predicted phases
Experimentally determined phases
Exp. compositions of phases (at.%) Bi (at.%)
Cu (at.%)
Sb (at.%)
39 Bi 18 Cu 43 Sb
Rhombo CUSB_ETA Liquid
Rhombo CUSB_ETA Liquid
28 e 68
3 66 7
69 34 25
62 Bi 19 Cu 19 Sb
CUSB_ETA Liquid
CUSB_ETA Liquid
e 82
66 5
34 13
11 Bi 80 Cu 9 Sb
FCC_A1 CUSB_DELTA Liquid
FCC_A1 CUSB_DELTA Liquid
e 1 90
97 80 7
3 19 3
112
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
for the constitutive binary systems from the literature. Predicted phase diagrams show good agreement with the experimental results.
Acknowledgements The authors are grateful to Dr. Jan Vrˇesˇˇta´l (Masaryk University Brno, Czech Republic) and Dr. Iwao Katayama (Department of Materials Science and Processing, Faculty of Engineering, Osaka University, Japan) for their help during the preparation of the paper. This work was supported by Ministry of Science and Environmental Protection of the Republic of Serbia (Project No. 142043). Calculations were performed by THERMOCALC software. This work was performed in the frame of the European action COST 531 on lead-free solder materials.
Fig. 2. Calculated isothermal section of the BieCueSb ternary system at 400 C with the EDX results (square-overall composition; triangle-composition of phase).
5. Conclusion Phase equilibria in the ternary system BieCueSb were investigated experimentally, using DTA and SEM/EDX. Four characteristic isopleths and isothermal section at 400 C were calculated using optimized thermodynamic parameters
References [1] [2] Dinsdale AT. SGTE DATA for pure elements. Calphad 1991;15:317e425. [3] Dinsdale AT, Kroupa A, Vı´zdal J, Vrestal J, Watson A, Zemanova A. COST531 Database for Lead-free Solders, Ver. 2.0, unpublished research, 2006. [4] Teppo O, Niemela J, Taskinen P. Report TKK-V-B50. Helsinki Univ.Tech.; 1989. [5] Ohtani H, Ishida K. J. Electron. Mater. 1994;23:747. [6] Liu XJ, Wang CP, Ohnuma I, Kainuma R, Ishida K. J. Phase Equilib. 2000;21(5):432e42.
Intermetallics 16 (2008) 107e112 www.elsevier.com/locate/intermet
Experimental study and thermodynamic calculation of BieCueSb system phase equilibria D. Manasijevic´ a,*, D. Minic´ b, D. Zˇivkovic´ a, D. Rajnovic´ c a University of Belgrade, Technical Faculty, VJ 12, 19210 Bor, Serbia University of Pristina, Faculty of Technical Science, 38220 Kosovska Mitrovica, Serbia c University of Novi Sad, Faculty of Technical Sciences, Trg D. Obradovic´a 6, 21000 Novi Sad, Serbia b
Received 5 January 2007; received in revised form 5 July 2007; accepted 15 August 2007 Available online 24 October 2007
Abstract Phase equilibria in the BieCueSb ternary system have been studied experimentally and calculated by the CALPHAD method. Three calculated vertical sections from bismuth corner with molar ratio of copper and antimony equal to 7/3, 1/1 and 3/7 and one vertical section from antimony corner with molar ratio of copper and bismuth equal to 1/1 were compared with the DTA results from this work. Calculated isothermal section at 400 C was compared with the results of SEM/EDX analysis from the present study. Reasonable agreement between calculations and experimental data was observed in all cases. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Ternary alloy systems; B. Phase diagrams; E. Phase diagram, prediction
1. Introduction The elements Bi, Cu and Sb are important for the design of microsoldering and substrate materials. Therefore, knowledge of the phase equilibria in the BieCueSb ternary system is desirable for the development of lead-free solder alloys. Thermodynamic modeling of phase equilibria in perspective systems represents first necessary step for development of new lead-free soldering materials. For this purpose, in the frame of COST 531 action [1] and SGTE, thermodynamic database based on recent version 4.4 SGTE [2] values of Gibbs energies for a pure element was developed [3]. It contains the data for carefully tested binary phase diagrams, suitable for prediction of phase equlibrium in multicomponent systems. In this paper, the BieCueSb ternary system is investigated via experiment and thermodynamic binary-based prediction according to CALPHAD technique. Calculated vertical sections
* Corresponding author. Tel./fax: þ381 30 424 547. E-mail address: [email protected] (D. Manasijevic´). 0966-9795/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2007.08.005
from bismuth and antimony corners and isothermal section at 400 C were compared with experimental results based on DTA and SEM/EDX from the present study. 2. Experimental procedure All samples were prepared from Bi, Cu and Sb shots of 99.99% purity. The samples, having masses approximately 5 g, were prepared in an induction furnace under high purity argon. As Sb is easy to volatilize, before melting an extra amount of Sb (about 3e5 wt.%) was added to compensate the weight loss. After melting, the samples were sealed in evacuated quartz tubes for homogenization heat treatment. The samples were annealed at 400 C for 200 h. After annealing, samples prepared for DTA measurements were gradually cooled down in order to obtain stable equilibrium at room temperature. Samples prepared for SEM/EDX investigation were quenched into ice water. The equilibrium compositions of phases were determined using JEOL JSM-6460 scanning electron microscope with accelerating voltage 20 kV and EDX analyzer.
108
Table 1 Optimized thermodynamic parameters for constitutive binaries used in this study Ref.
G(LIQUID,BI;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ þ3428.29 þ 107.782416*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 5.9549E 19*T7 (298.14 < T < 544.54) þ41544.282 414.460769*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3616168*T(1) (544.54 < T < 800.00) þ290.595 þ 161.738553*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 (800.00 < T < 1200.00) þ3754.947 þ 103.961021*T 27.196*T*LN(T ) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
G(LIQUID,CU;0) H298(FCC_A1, CU;0)¼ þ5194.277 þ 120.973331*T 24.112392*T*LN(T ) 0.00265684*T2 þ 1.29223E 07*T3 þ 52478*T(1) 5.8489E 21*T7 (298.14 < T < 1357.77) 46.545 þ 173.881484*T 31.38*T*LN(T ) (1357.77 < T < 3200.00)
[2,3] [2,3]
G(LIQUID,SB;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ þ10579.47 þ 134.231525*T 30.5130752*T*LN(T ) þ 0.007748768*T2 3.003415E 06*T3 þ 100625*T(1) 1.74847E 20*T7 (298.14 < T < 903.78) þ8175.359 þ 147.455986*T 31.38*T*LN(T ) (903.78 < T < 2000.00) L(LIQUID,BI,CU;0) ¼ þ 20,747.5 5.85*T L(LIQUID,BI,CU;1) ¼ 4925 þ 2.55*T L(LIQUID,BI,CU;2) ¼ þ4387.5 2.3*T L(LIQUID,BI,SB;0) ¼ þ2230 þ 0.06*T L(LIQUID,CU,SB;0) ¼ 16,154.82 þ 23.99549*T 4.0284*T*LN(T ) L(LIQUID,CU,SB;1) ¼ 35,130.8 þ 50.3301*T 5.2316*T*LN(T ) L(LIQUID,CU,SB;2) ¼ 29,263.28 þ 15.3192*T L(LIQUID,CU,SB;3) ¼ 2300.89 L(LIQUID,CU,SB;4) ¼ 8873.94
[2,3] [2,3] [3,4] [3,4] [3,4] [3,5] [3,6] [3,6] [3,6] [3,6] [3,6]
FCC_A1 2 SUBLATTICES, SITES 1:1 CONSTITUENTS: BI,CU,SB: VA G(FCC_A1,BI:VA;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ þ2082.224 þ 115.918925*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 (298.14 < T < 544.54) þ40108.022 406.150351*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3616168*T(1) þ 1.66145E þ 25*T(9) (544.54 < T < 800.00) 1145.664 þ 170.048971*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 þ 1.66145E þ 25*T(9) (800.00 < T < 1200.00) þ2318.688 þ 112.27144*T 27.196*T*LN(T ) þ 1.66145E þ 25*T(9) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
G(FCC_A1, CU:VA;0) H298(FCC_A1, CU;0)¼ 7770.458 þ 130.485235*T 24.112392*T*LN(T ) 0.00265684*T2 þ 1.29223E07*T3 þ 52478*T(1) (298.14 < T < 1357.77) 13542.026 þ 183.803828*T 31.38*T*LN(T ) þ 3.64167E þ 29*T(9) (1357.77 < T < 3200.00)
[2,3] [2,3]
G(FCC_A1, SB:VA;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ þ10631.142 þ 142.454689*T 30.5130752*T*LN(T ) þ 0.007748768*T2 3.003415E 06*T3 þ 100625*T(1) (298.14 < T < 903.78) þ 8135.17 þ 155.785872*T 31.38*T*LN(T ) þ 1.616849E þ 27*T(9) (903.78 < T < 2000.00) L(FCC_A1,BI,CU:VA;0) ¼ þ50*T L(FCC_A1,BI,SB:VA;0) ¼ þ10,150 6.3*T L(FCC_A1,CU,SB:VA;0) ¼ 8534 10.44293*T
[2,3] [2,3] [3] [3] [3,6]
BCC_A2 2 SUBLATTICES, SITES 1:3 CONSTITUENTS: BI,CU,SB:VA G(BCC_A2,BI:VA;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ þ3479.224 þ 114.518925*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 (298.14 < T < 544.54) þ41505.022 407.550351*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3,616,168*T(1) þ 1.66145E þ 25*T(9) (544.54 < T < 800.00) þ251.336 þ 168.648971*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 þ 1.66145E þ 25*T(9) (800.00 < T < 1200.00) þ3715.688 þ 110.87144*T 27.196*T*LN(T ) þ 1.66145E þ 25*T(9) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
LIQUID CONSTITUENTS: BI,CU,SB
[2,3] [2,3]
G(BCC_A2, SB:VA;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ þ10631.142 þ 141.054689*T 30.5130752*T*LN(T ) þ 0.007748768*T**2 3.003415E 06*T3 þ 100625*T(1) (298.14 < T < 903.78) þ8135.17 þ 154.385872*T 31.38*T*LN(T ) þ 1.616849E þ 27*T(9) (903.78 < T < 2000.00) L(BCC_A2,BI,CU:VA;0) ¼ þ50*T L(BCC_A2,BI,SB:VA;0) ¼ þ10,150 6.3*T L(BCC_A2,CU,SB:VA;0) ¼ þ50,092.341 41.561183*T L(BCC_A2,CU,SB:VA;1) ¼ 331,192.835 þ 110.62385*T L(BCC_A2,CU,SB:VA;2) ¼ þ301,571.206 þ 15*T L(BCC_A2,CU,SB:VA;3) ¼ 984.45639 77.2521*T L(BCC_A2,CU,SB:VA;4) ¼ 90*T
[2,3] [2,3] [3] [3] [3,6] [3,6] [3,6] [3,6] [3,6]
RHOMBOHEDRAL_A7 CONSTITUENTS: BI,SB G(RHOMBOHEDRAL_A7,BI;0) H298(RHOMBOHEDRAL_A7,BI;0)¼ 7817.776 þ 128.418925*T 28.4096529*T*LN(T ) þ 0.012338888*T2 8.381598E 06*T3 (298.14 < T < 544.54) þ30,208.022 393.650351*T þ 51.8556592*T*LN(T ) 0.075311163*T2 þ 1.3499885E 05*T3 3,616,168*T(1) þ 1.66145E þ 25*T(9)(544.54 < T < 800.00) 11,045.664 þ 182.548971*T 35.9824*T*LN(T ) þ 0.0074266*T2 1.046E 06*T3 þ 1.66145E þ 25*T(9) (800.00 < T < 1200.00) 7581.312 þ 124.77144*T 27.196*T*LN(T ) þ 1.66145E þ 25*T(9) (1200.00 < T < 3000.00)
[2,3] [2,3] [2,3] [2,3]
G(RHOMBOHEDRAL_A7, SB;0) H298(RHOMBOHEDRAL_A7,SB;0)¼ 9242.858 þ 156.154689*T 30.5130752*T*LN(T ) þ 0.007748768*T2 3.003415E 06*T3 þ 100625*T(1) (298.14 < T < 903.78) 11738.83 þ 169.485872*T 31.38*T*LN(T ) þ 1.616849E þ 27*T(9) (903.78 < T < 2000.00) L(RHOMBOHEDRAL_A7,BI,SB;0) ¼ þ 10,150 6.3*T L(RHOMBOHEDRAL_A7,BI,SB;1) ¼ 150
[2,3] [2,3] [3,5] [3,5]
CUSB_ZETA 2 SUBLATTICES, SITES 0.77:0.23 CONSTITUENTS: CU:SB G(CUSB_ZETA,CU:SB;0) 0.77H298(FCC_A1,CU;0) 0.23H298(RHOMBOHEDRAL_A7,SB;0) ¼ 4936.60.94*T þ 0.77*GHSERCU þ 0.23*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_GAMMA 2 SUBLATTICES, SITES 0.85:0.15 CONSTITUENTS: CU:SB G(CUSB_GAMMA,CU:SB;0) 0.85H298(FCC_A1,CU;0) 0.15H298(RHOMBOHEDRAL_A7,SB;0) ¼ 26801.8*T þ 0.85*GHSERCU þ 0.15*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_ETA 2 SUBLATTICES, SITES 0.67:0.33 CONSTITUENTS: CU:SB G(CUSB_ETA,CU:SB;0) 0.67H298(FCC_A1,CU;0) 0.33H298(RHOMBOHEDRAL_A7,SB;0) ¼ 4350.7723.888*T þ 0.67*GHSERCU þ 0.33*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_EPSILON 2 SUBLATTICES, SITES 0.75:0.25 CONSTITUENTS: CU:SB G(CUSB_EPSILON,CU:SB;0) 0.75H298(FCC_A1,CU;0) 0.25H298(RHOMBOHEDRAL_A7,SB;0) ¼ 4718 1.69*T þ 0.75*GHSERCU þ 0.25*GHSERSB (298.14 < T < 3000.00)
[3,6]
CUSB_DELTA 2 SUBLATTICES, SITES 0.8:0.2 CONSTITUENTS: CU:SB G(CUSB_DELTA,CU:SB;0) 0.8H298(FCC_A1,CU;0) 0.2H298(RHOMBOHEDRAL_A7,SB;0) ¼ 5142 þ 0.8*GHSERCU þ 0.2*GHSERSB (298.14 < T < 3000.00)
[3,6]
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
G(BCC_A2, CU:VA;0) H298(FCC_A1,CU;0)¼ 3753.458 þ 129.230235*T 24.112392*T*LN(T )0.00265684*T2 þ 1.29223E07*T3 þ 52478*T(1) (298.14 < T < 1357.77) 9525.026 þ 182.548828*T 31.38*T*LN(T ) þ 3.64167E þ 29*T(9) (1357.77 < T < 3200.00)
109
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110
Table 2 DTA results for the investigated alloys of the BieCueSb ternary system Sample composition (at.%)
Thermal effect ( C) Liquidus temperature
Other peak temperature
Cu:Sb ¼ 7:3 Bi10Cu63Sb27 Bi20Cu56Sb24 Bi30Cu49Sb21 Bi40Cu42Sb18 Bi50Cu35Sb15 Bi60Cu28Sb12 Bi70Cu21Sb9 Bi80Cu14Sb6 Bi95Cu3.5Sb1.5
649 642 650 654 657 662 655 646 494
269, 278, 284, 282, 294, 283,
406, 414, 406, 423, 425, 422, 268, 273,
555 525 521 512 532 513 485 426 286
Cu:Sb ¼ 1:1 Bi10Cu45Sb45 Bi20Cu40Sb40 Bi30Cu35Sb35 Bi40Cu30Sb30 Bi50Cu25Sb25 Bi60Cu20Sb20 Bi70Cu15Sb15 Bi80Cu10Sb10 Bi90Cu5Sb5
582 573 596 621 641 647 658 646 581
419, 353, 347, 415, 333, 316, 306, 298, 282, 280,
492 451 569 574 561 547 539 520 488
Cu:Sb ¼ 3:7 Bi10Cu27Sb63 Bi20Cu24Sb56 Bi30Cu21Sb49 Bi40Cu18Sb42 Bi50Cu15Sb35 Bi60Cu12Sb28 Bi70Cu9Sb21 Bi80Cu6Sb14 Bi90Cu3Sb7
507 552 538 561 572 564 555 524 492
e 394, 363, 312, 299, 295,
478 463 437 361 336 302 294 288
Bi:Cu ¼ 1:1 Bi45Cu45Sb10 Bi40Cu40Sb20 Bi35Cu35Sb30 Bi30Cu30Sb40 Bi25Cu25Sb50 Bi20Cu20Sb60 Bi15Cu15Sb70 Bi10Cu10Sb80 Bi5Cu5Sb90
632 657 629 586 548 506 515 565 593
270, 383, 472, 583 279, 424, 492 293, 379, 564 303, 454 384, 497 e 452 522 513
DTA measurements were carried out with the Derivatograph (MOM Budapest) apparatus under following conditions: argon atmosphere, heating rate 5 C/min using sintered Al2O3 as the reference specimen. 3. Thermodynamic modeling The pure solid elements in their stable form at 298.15 K and under the pressure of 1 bar were chosen as the reference state for the systems (SER). The Version 4.4 of the SGTE Unary Database (Scientific Group Thermodata Europe) of phase stabilities for stable and metastable states of pure elements [2] was used. Thermodynamic data for the BieCu system were taken from Ref. [4], for the BieSb system were published in
Ref. [5], and thermodynamic data for the system CueSb were taken from Ref. [6]. All these data are included in the COST 531 Database for Lead-Free Solders [3]. The following phases from constitutive binary subsystems were considered for thermodynamic binary-based prediction: liquid phase, the Cu-based fcc solution (denoted as FCC_A1), Sb and Bi rich solid solution (denoted as RHOMBOHEDRAL_A7), b phase with bcc structure (denoted as BCC_A2 phase), z (Cu10Sb3), g (Cu17Sb3), h (Cu2Sb), 3 (Cu3Sb), and d (Cu4Sb) intermediate phases from CueSb binary systems with very narrow concentration ranges of existence denoted as: CUSB_ZETA, CUSB_GAMMA, CUSB_ETA, CUSB_ EPSILON, and CUSB_DELTA, respectively. The Gibbs energies of the liquid, fcc, bcc and rhombo phases are described by a substitution solution model and a RedlicheKister formalism. All of the compounds were treated as stoichiometric compounds. Phase diagram of the BieCueSb ternary system was calculated using only optimized thermodynamic parameters for constitutive binary systems. No further thermodynamic optimization was done in the present work. Optimized thermodynamic parameters of constitutive binary systems used for calculation are shown in Table 1. 4. Results and discussion 4.1. Isopleths (vertical sections) Four characteristic isopleths of the BieCueSb ternary system were experimentally investigated by DTA. The analysis of DTA measurements was performed on DTA curves obtained during the heating of samples. Temperatures of phase transitions were read using software delivered with the instrument. The results are shown in Table 2. Mutual comparison between DTA results and calculated phase diagrams is presented in Fig. 1. It can be seen that there is a reasonable agreement between DTA results from this work and calculated phase diagrams for all investigated isopleths. Calculated liquidus temperatures are confirmed quite well by DTA measurements. Calculated vertical section with molar ratio Cu:Sb ¼ 7:3 includes three primary crystallization areas (liquid þ BCC_A2; liquid þ CUSB_DELTA and very narrow primary crystallization region of liquid þ Rhombo (Bi)), vertical section with molar ratio Cu:Sb ¼ 1:1 includes four primary crystallization areas (liquid þ BCC_A2; liquid þ CUSB_DELTA; liquid þ CUSB_ETA and narrow liquid þ Rhombo (Bi)), vertical section with molar ratio Cu:Sb ¼ 3:7 includes three primary crystallization areas (liquid þ BCC_A2; liquid þ Rhombo; liquid þ CUSB_ETA) and vertical section from antimony corner with molar ratio Bi:Cu ¼ 1:1 includes four primary crystallization areas (liquid þ FCC_A1, liquid þ BCC_A2; liquid þ Rhombo; liquid þ CUSB_ETA). 4.2. Isothermal section at 400 C The SEM (scanning electron microscope) with EDX (energy dispersive X-ray) analyzer was used for determination
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
111
Fig. 1. .Calculated vertical sections of the BieCueSb ternary system with DTA results from the present study: (a) Cu:Sb ¼ 7:3, (b) Cu:Sb ¼ 1:1, (c) Cu:Sb ¼ 3:7 and (d) Bi:Cu ¼ 1:1.
of composition of coexisting phases at 400 C. Two quenched samples with predicted three-phase structure and one sample with predicted two-phase structure were analyzed. All results from SEM analysis are given in the Table 3. Comparison of calculated phase diagram of the BieCueSb ternary system at 400 C with experimental results from this work is shown in Fig. 2. Predicted phase structure was experimentally confirmed for all three analyzed samples. Experimentally determined
compositions of CUSB_ETA and CUSB_DELTA phases are in good agreement with calculated phase diagram as well as determined solubility of antimony in the fcc copper-rich phase. Former liquid phase had very inhomogeneous structure and strong dispersion of obtained results by EDX point analysis with large experimental error (up to 4 at.%) were noticed. These large standard errors were probably caused by decomposition of equilibrated liquid during quick cooling and solidification.
Table 3 Results of the SEM-EDX analysis at 400 C Overall experimental composition (at.%)
Theoretically predicted phases
Experimentally determined phases
Exp. compositions of phases (at.%) Bi (at.%)
Cu (at.%)
Sb (at.%)
39 Bi 18 Cu 43 Sb
Rhombo CUSB_ETA Liquid
Rhombo CUSB_ETA Liquid
28 e 68
3 66 7
69 34 25
62 Bi 19 Cu 19 Sb
CUSB_ETA Liquid
CUSB_ETA Liquid
e 82
66 5
34 13
11 Bi 80 Cu 9 Sb
FCC_A1 CUSB_DELTA Liquid
FCC_A1 CUSB_DELTA Liquid
e 1 90
97 80 7
3 19 3
112
D. Manasijevic´ et al. / Intermetallics 16 (2008) 107e112
for the constitutive binary systems from the literature. Predicted phase diagrams show good agreement with the experimental results.
Acknowledgements The authors are grateful to Dr. Jan Vrˇesˇˇta´l (Masaryk University Brno, Czech Republic) and Dr. Iwao Katayama (Department of Materials Science and Processing, Faculty of Engineering, Osaka University, Japan) for their help during the preparation of the paper. This work was supported by Ministry of Science and Environmental Protection of the Republic of Serbia (Project No. 142043). Calculations were performed by THERMOCALC software. This work was performed in the frame of the European action COST 531 on lead-free solder materials.
Fig. 2. Calculated isothermal section of the BieCueSb ternary system at 400 C with the EDX results (square-overall composition; triangle-composition of phase).
5. Conclusion Phase equilibria in the ternary system BieCueSb were investigated experimentally, using DTA and SEM/EDX. Four characteristic isopleths and isothermal section at 400 C were calculated using optimized thermodynamic parameters
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