Activity Measurement of the Constituents in Molten Sn Mg Zn Ternary Lead Free Solder Alloys by Mass Spectrometry

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1 Materials Transactions, Vol. 43, No ) pp to 3233 c 22 The Japan Institute of Metals Activity Measurement of the Constituents in Molten Ternary Lead Free Solder Alloys by Mass Spectrometry Naotaka Ogawa 1, 1, Takahiro Miki 1, Tetsuya Nagasaka 1 and Mitsutaka Hino 1 1 Department of Metallurgy, Graduate School of Engineering, Tohoku University, Sendai , Japan Activities of the constituents in an alloy proposed for the Pb-free solder,, were studied experimentally using a mass spectrometer. The ion current ratios of to were measured in the temperature range 7 8 K. From the experimental results and the assessed thermodynamic properties of molten,, and binary alloys, the excess Gibbs free energy of liquid ternary alloy was determined. Also, phase diagram of ternary system was determined. Received July 26, 22; Accepted October 16, 22) Keywords: mass spectrometry, thermodynamics, lead-free solder, Tin Magnesium Zinc ternary alloy, activity, excess Gibbs free energy, interaction parameter, phase diagram 1. Introduction The increase of demand for smaller and lighter portable electronic devices has made interconnecting densities and packaging technologies more important. Soldering material widely used is Pb alloy, which have low melting point and excellent electrical, strength properties and wettability. However, Pb is one of the toxic elements, which is undesirable due to environmental and safety reasons, thus Pb-free alternative alloy is preferred for a new soldering material. based alloys were viewed as very promising cadidates 1) among many potential substitutes, and alloy has been already used as a soldering alloy in limited proposes. Addition of to alloy decreases the melting point of the alloy, hence alloy is expected to be suitable for replacing Pb solder alloy. In order to design new Pb-free soldering materials, precise understanding of thermodynamic properties and phase diagrams for alloy systems are crucial. The thermodynamic properties of, 2 7), 8 11) and 12 18) binary systems have been researched by many researchers. Also, the phase diagrams of these binary systems 19 21) were assessed using CALPHAD approach. 22) However, the thermodynamic properties of liquid phases determined experimentally do not accord with that obtained by phase diagram assessment, in general. This discrepancy arises because the thermodynamic properties of liquid phases were not considered properly during the phase diagram assessment. It is important to assess the phase diagram by considering the activity of constituents in liquid phase. Also, accurate information for thermodynamic properties of liquid phases is indispensable for compatible phase diagram assessment. Hence, in the present work, the activities of the constituents in alloy were measured. In the present work, the ion current ratios of to were measured for alloy by mass spectrometry. The mass spectrometry method was selected because vapor pressure of and were relatively high, and accurate measurement could be expected. Moreover, the activities of all 1 Formerly Graduate Student, Tohoku University. Present address: Fukuyama Works, NKK Corporation, Fukuyama , Japan. constituents at various temperature could be determined by measuring only the ion current ratios of to. Also, the authors reviewed the thermodynamic properties of liquid,, and binary alloy determined by the other researchers and evaluated a thermodynamic function to express the excess Gibbs free energy of each binary alloy. Thermodynamic function to express the excess Gibbs free energy of liquid ternary alloy was determined, utilizing the assessed Gibbs free energy of terminal binary alloys with the measured ion current ratios using mass spectrometer. From the present results, the equilibrium phase diagram for ternary was calculated. 2. Experimental The mass spectrometer used in the present work was the same with that used in our previous work. 23) This equipment was a magnetic field scanning type model, which had single focusing 9 and.2 m radius of curvature. This mass spectrometer consists of a Knudsen cell unit, an ionization chamber, a magnetic field scanning system and a detection unit with electron multiplier. The atomic or molecular beam effused from the Knudsen cell was conducted directly into the ionization chamber, where kinds of the metal vapor were converted into positive ions by electron impact. The positive ions were then pulsed out of the ion source and accelerated down the flight tube for analysis. An ionization potential and an ion accelerating voltage were generally 2 ev and 12. kv, respectively. The masses were separated with scanning a magnetic field and detected by a secondary electron multiplier. The intensity of scanning magnetic field was in the range of.4 to 1.55 T. An analog output circuit was used to detect and display the mass peaks on a monitor or penrecorder. Inside of the system was evacuated by rotary and diffusion pumps to approximately Pa. The Knudsen cell assembly consisted of a Ta outer cell with an Al 2 O 3 inner cell, which held approximately 1.5 g of the alloy sample. The Al 2 O 3 inner cell had a dimension of 11 mm in O.D., 9 mm in I.D. and 7 mm in height, and the lid had a thickness of.5 mm and an orifice diameter of.5 mm. Heat-

2 3228 N. Ogawa, T. Miki, T. Nagasaka and M. Hino Table 1 Linear relation of lni + /I + ) lnx /X In ) versus 1/T for the system. Average Initial Final lni + /I + ) lnx /X ) composition composition composition =A BT 1 X X X X X X X X X A B ±1.93).449 ±.149) ±4.84).459 ±.372) ±2.4).569 ±.156) ±.73).563 ±.537) ±1.8).548 ±.834) ±.696).515 ±.523) ±.32).515 ±.243) ±.843).52 ±.646) ±1.28).337 ±.975) ±1.68).382 ±.128) ±.458).381 ±.35) ±1.2).412 ±.922) ±.26).35 ±.2) ±1.38).959 ±.15) ±2.49) 1.45 ±.191) ing of the Knudsen cell was made by means of electric resistance heating element of Ta ribbon heater. The temperature of the Knudsen cell was measured by two sets of Pt-13pctRh/Pt thermocouple, which were respectively placed in two holes drilled at the bottom of the Ta outer cell with different depth. Calibration of the thermocouple was periodically performed by wire bridge technique using Au. Weighed pure metals were charged in the Al 2 O 3 inner cell, and the whole Knudsen cell assembly was positioned at 5 to 6 cm below the ionizing region of the mass spectrometer and was adjusted horizontally to maximize the flux of particles into the ion source by maximizing the ion currents. The cell was then heated above the liquidus temperature of the alloy specimen and held for 1 15 min at the aimed temperature to allow melting and homogenization of the alloy. Control of the current for Ta heater was achieved manually to adjust the temperature of the cell. The ion currents at desired principal mass peaks were monitored on the CRT of a personal computer and recorded on a calibrated chart recorder. In the present work, ion currents of mass number 24 + ) and 64 + ) were measured in the temperature range of 7 8 K. The measurements were conducted by decreasing the experimental temperature from approximately 8 K. The holding time of 1 min at each temperature was found to be sufficient to obtain constancy of ion current and the measurement was completed within 2 h. After the measurement, the sample was quenched to the room temperature in the mass spectrometer and was supplied for chemical analysis of the composition. 3. Results and Discussion The composition of the alloy sample changed during the experiment due to evaporation. The weight loss of at time t was calculated by the following procedure. Relation among the monitored ion current of 64 + ), I +, sample temperature, T, and total weight decrease of the alloy during lni / I ) - lnx / X ) X =.374 X =.387 X =.452 X /X = T -1 / K -1 X =.56 X =.573 Fig. 1 Temperature dependence of lni /I ) lnx /X ) for alloy at X /X = the experiment from time to t fin, W, can be expressed as eq. 1). W = k t=t fin t= I + T )dt 1) Constant k was derived for each measurement, and the alloy composition during the experiment was determined by utilizing eq. 1). The experimental results are shown in Table 1. Also, the experimental results for alloy at X / X = are shown in Fig. 1. Linear relation was observed between lni + /I + ) lnx / X ) and the reciprocal of ab-

3 Activity Measurement of Molten Ternary Alloy by Mass Spectrometry 3229 solute temperature. lni + /I + ) lnx / X ) = A + BT 1 2) Here, I + i is ion current of i. The values of A and B regressed with the least-squares method for system are listed in Table 1. The adopted composition shown in Table 1 is the average composition during the measurement. The compositions before and after the experiment are also shown. The numerals in parentheses are standard deviation. The excess free energy change of mixing for alloy was approximated by the substitutional subregular solution model 24, 25) as follows, G ex = n n+1 i=1 j=i+1 Ω i j X i X j + Ω i j k X i X j X k. 3) i j=i+1 k= j+1 Where Ω i j and Ω i j k are binary and ternary interaction parameters between i and j atoms and among i, j, and k atoms, respectively. The effects of composition and temperature on Ω i j and Ω i j k are expressed as follows, 26) Ω i j = n n Ω i j X i X j ) n n =, 1, 2,...), 4) RT ln l) / kj -3 Sharma 173K) Eckert et al. 173K) Egan 173K) Eldridge et al. 143K) Moser et al. 173K) Present work 173K) X ) 2 Fig. 2 Relation between 1 X ) 2 and RT ln γ in binary system. Moser 68K) Moser 88K) Chiotti et al. 68K) Chiotti et al. 88K) Vyazner et al. 12K) Agarwal et al. 88K) Present work 88K) Ω i j k = Ω i j k X i + 1 Ω i j k X j + 2 Ω i j k X k, 5) n Ω i j = n A + n BT + n CT ln T 6) n Ω i j k = n A + n B T + n C T ln T 7) The interaction parameters for n Ω i j in each terminal binary system were evaluated by using the literature, as explained in the following. The activity coefficient of component in molten,, binary alloys is shown in Figs Each dot represents the experimentally measured value and curves represent the activity coefficients of elements evaluated with phase diagram assessment by present authors. The reported activity coefficient of in binary alloy agrees with each other. In the present work, interaction parameters were determined by using the experimental results of Sharma, 2) and heat of mixing reported by Nayeb-Hashemi and Clark. 7) As the reported activity coefficient of in binary alloy does not agree with each other, thermodynamic function for expressing the excess Gibbs free energy change for mixing and 11) was used in the present work. The authors considered that the selected thermodynamic function is reasonable, because it agrees with the results of Chiotti et al. 1) at 68 and 88 K and that of Moser 8) at 88 K. For binary, the assessed values reported by Hultgren et al. 12) at 7 K was used for interaction parameters determination. The values assessed by Hultgren et al. satisfy with the experimental results, except for that of Nakamura et al. 14) Also, the selected value agrees with the assessed thermodynamic function of Ototani et al., 21) especially where concentration is high. The interaction parameters obtained and used in the present work are listed in Table 2. The ternary interaction parameter for alloy, has been unknown. Here it is assumed that Ω i j k, 1 Ω i j k, and 2 Ω i j k were equivalent values. Partial excess free energy of mixing for ternary alloy, which RT ln l) / kj X ) 2 Fig. 3 Relation between 1 X ) 2 and RT ln γ in binary system. Fig. 4 RT ln l) / kj Hultgren 7K) Fioriani et al. 75K) Jellinek et al. 973K) Jellinek et al. 158K) Nakamura et al. 7K) Scheil et al. 73K) Scheil et al. 723K) Scheil et al. 798K) Scheil et al. 873K) Burmeister et al. 957K) Ohtani et al. 7K) Present work 7K) X ) 2 Relation between 1 X ) 2 and RT ln γ in binary system.

4 323 N. Ogawa, T. Miki, T. Nagasaka and M. Hino Table 2 Interaction parameters in,, and binary alloys. System Ω i j /J mol 1 1 Ω i j /J mol 1 2 Ω i j /J mol 1 3 Ω i j /J mol 1 2, 7) T T T T 11) T T ln T T ) T T T T consists of components 1, 2, and 3, can be expressed as eqs. 8) 1). 1 = G ex G ex Gex X 2 X 3 8) X 2 X 3 2 = Gex + 1 X 2 ) Gex G ex X 3 9) X 2 X 3 3 = G ex Gex X X 3 ) Gex 1) X 2 X 3 Substituting components 1, 2 and 3 with, and, respectively, the following relations can be derived. = G ex G ex Gex X X 11) X X = Gex + 1 X ) Gex G ex X 12) X X = G ex Gex X + 1 X ) Gex 13) X X Hence, the difference between the activity coefficients of and can be expressed as follows, RT ln γ ln γ ) = Ḡex = X { Ω + 1 Ω 2X X ) + 2 Ω X X )3X X ) + 3 Ω X X ) 2 4X X )} + Ω X + X ) + 1 Ω X 2 + 4X X X 2 ) + 2 Ω X X ) X 2 + 6X X X 2 ) + X { Ω + 1 Ω X + 2X ) + 2 Ω X X ) X + 3X ) + 3 Ω X X ) 2 X + 4X )} + Ω X X + X ). 14) The chemical reaction and equilibrium constant, K, in the mass spectrometry experiment can be expressed as follows, because vapor pressure of is negligible small. Ml) = Mg)M :, ) 15) K = P ) M = exp Govap M. 16) γ M X M RT Here, P M and G ovap M are the partial vapor pressure of M and the standard Gibbs free energy change of eq. 15), respectively. When the effusion of vapor from the Knudsen cell orifice satisfies molecular flow conditions, the relation between ion current and partial vapor pressure can be written as follows, P M = k M I + MT. 17) Here, I + M is the ion current of M and k M is the constant, which includes apparatus constant and ionization cross section, and they are independent of temperature and alloy composition. Substituting and for M in eqs. 16) and 17) and combining and rearranging them derives eq. 18). ) RT ln γ ln γ ) = RT ln I + I + ln X X + G ovap Govap + RT ln k k 18) Combining eq. 14) with 18) and rearranging them deduces eq. 19). Y RT ln I + I + ln X ) X X { Ω + 1 Ω 2X X ) + 2 Ω X X )3X X ) + 3 Ω X X ) 2 4X X )} Ω X + X ) 1 Ω X 2 + 4X X X 2 ) 2 Ω X X ) X 2 + 6X X X 2 ) X { Ω + 1 Ω X + 2X ) + 2 Ω X X ) X + 3X ) + 3 Ω X X ) 2 X + 4X )} + Ω X X + X ) = Ω X X + X ) G ovap Govap + RT ln k ). 19) k Y should be a linear function of X X + X ) at each constant temperature when eq. 19) is reasonable. Figure 5 represents the plot of Y against X X + X ) at 773 K. It can be seen from this figure that the values of Y are almost linear with X X + X ), and the slope of the regression )

5 Activity Measurement of Molten Ternary Alloy by Mass Spectrometry = ) / J mol -1.9 Y / kj mol X -X X ) Fig. 5 Determination of ternary interaction parameter Ω at 773 K. Fig. 7 Iso-activity curves of in liquid alloy. The standard state is pure liquid at 773 K. -- / kj mol = T 474) / J mol T / K Fig. 6 Temperature dependence of ternary interaction parameter Ω. Fig. 8 Iso-activity curves of in liquid alloy. The standard state is pure liquid at 773 K. line corresponds to the value of ternary interaction parameter, Ω, at 773 K. The value of Ω at 773 K was determined as 349±474)/J mol 1. The value in parenthesis is standard deviation. Temperature dependence of the ternary interaction parameter, Ω is shown in Fig. 6. The ternary interaction parameter was determined as a function of temperature as eq. 2), using least-squares method. Ω = T ±474)/J mol 1 2) The activity curve of each component of alloy at 773 K is calculated by eq. 2) analysis and is shown in Figs The numerals in the figures indicate the activities of the components. The activity of in alloy is shown in Fig. 7. The activity of increases with substituting with at constant mole fraction. This is reasonable because intermetallic compound exists except for binary system, the attractive force between and is expected to be larger than that between and. The activity of in alloy is shown in Fig. 8. The activity of is nearly constant when substituting with at constant mole fraction in the rich liquid range where mole fraction is lower than.5. On the other hand, activity decreases in the composition region near the binary system. This is apprehensible by considering that the attractive force between and is expected to be larger than that between and. The activity of in alloy is shown in Fig. 9. The activity of is relatively small value near the binary, because has strong affinity with both and. Hence, addition of into binary alloy to lower the melting point could be easily carried out. The phase diagram of this system is evaluated from minimization of compared Gibbs free energy of each appearing possible phase and is shown in Fig. 1. The Gibbs free energies of formation for 2, 2 and 2 3 were estimated by considering equilibrium of the constituents in molten or binary alloys with each compounds at liquidus, and were determined as eqs. 21) 23). The values in parenthesis are standard deviation. The Gibbs free energies of formation for 2 and 2 3 were determined

6 3232 N. Ogawa, T. Miki, T. Nagasaka and M. Hino Table 3 Initial composition and composition of the liquidus equilibrating with 2 at 673 K..1 X X X Initial composition Composition of liquid phase Table 4 Experimental result of DTA. Temperature K) Sample X X X Endothermic Exothermic No. peak peak heating period) cooling period) , , 454 Fig. 9 Iso-activity curves of in liquid alloy. The standard state is pure liquid at 773 K K 573K 473K 673K 973K 873K 623K 74K 71K 471K 773K 455K 573K Composition of sample used in DTA. Composition of sample used in EPMA. Composition of solid phase from EPMA at 673K. Composition of liquid phase from EPMA at 673K. 621K 614K Fig. 1 Composition of sample used in EPMA and DTA and the result of EPMA. with excellent accuracy. G f 2 = 98784±4348) ±5.446)T/J 21) G f 2 = 5843±52) ±.7)T/J 22) G f 2 3 = 1833±9) ±.132)T/J 23) Solid solubility in, and phase was neglected, and 2 and 2 were assumed to be stoichiometric compound. The compounds 2 and 2 are very stable and these compounds control the shape of the liquidus curve. The eutectic temperature of the ternary alloy is 455 K, which is close to the eutectic temperature of Pb alloy. Hence, ternary eutectic alloy can be a substitute of Pb alloy, on the view of melting point of the solder alloy. Verification of the obtained phase diagram was conducted by analyzing the composition of the liquidus, which was equilibrated with 2 at 673 K for 778 ks in a vacuum-sealed pyrex tube. The composition of the liquidus was analyzed by EPMA. Compositions of the initial alloy and liquidus are shown in Table 3 and Fig. 1. From the EPMA analysis, no ternary intermetallic compound was observed and it was confirmed that the precipitated phase equilibrated with liquid phase was 2. The composition of the liquid phase was in accord with the liquidus line at 673 K. Also, DTA analysis was conducted to determine the liquidus temperature and the eutectic temperature. The alloy composition and the temperatures where endothermic and exothermic peak observed are shown in Table 4 and Fig. 1. The temperatures, 553 K and 523 K, where first exothermic peak was observed in the cooling period, were consistent with the liquidus temperature. Also, temperatures, 455 K and 453 K, where endothermic peak were observed, was very close to the eutectic temperature, 455 K, determined in the present work. The later temperature, which exothermic peak was observed during cooling period for sample No. 1, was 7 K lower than the determined eutectic temperature. The reason for this disagreement is probably due to super-cooling. From the results of EPMA and DTA analysis, the phase diagram of ternary system was verified to be reasonable. The excess free energy change of mixing ternary alloys was expressed as a function of alloy composition and temperature in the present work. Utilization of mass spectrometry will be a powerful method to determine the thermodynamic properties of molten alloys with high accuracy. The eutectic temperature of ternary alloy is comparable with that of Pb eutectic alloy, hence ternary alloy is suitable for alternative solder alloy, on the viewpoint of melting point of the alloy. 4. Conclusions The interaction parameters for liquid alloy were determined from the present experimental results and assessed thermodynamic properties of molten,, and binary alloys. Also, the phase diagram for ternary system was determined by the excess Gibbs free energy of mixing of liquid alloy, and it was verified that the determined phase diagram was suitable. Eutectic temperature of ternary alloy is comparable with that of Pb alloy, hence alloy is a candi-

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