An investigation on surface tensions of Pb-free solder materials

Surface tensions of some Pb-free solder systems such as Ag–Bi–Sn with cross-sections Ag/Bi = 1/1, Ag/Bi = 1/2, Ag/Bi = 2/1, In–Sn–Zn with cross-sections Sn/In = 1/1, Sn/In = 1/3 and (Ag₇Cu₃)_100?x Sn_x with cross-section Ag/Cu = 7/3 are calculated from the sub-binary surface tension data using the models, such as the Muggianu, Kohler, Toop models, Butler’s equation and Chou’s General Solution Model (GSM) at 873, 923 and 1073 K, respectively. The surface tension of In–Sn–Zn increases wavily with increasing amount of Zn and it is found that the best models are the GSM for both cross-sections in question while GSM becomes the best model for (Ag₇Cu₃)_100?x Sn_x alloy in the whole experimental range. Moreover, the surface tension of (Ag₇Cu₃)_100?x Sn_x decreases slightly with increasing amount of Sn. The Muggianu, Butler and Butler models are determined as the best models for the cross-sections in the order given above for entire measurement range, respectively, and the surface tension of Ag–Bi–Sn decreases slightly with an increasing amount of Bi and Ag but increases with increasing Sn in liquid alloys.     

Determination of surface tension of liquid ternary Ni–Cu–Fe and sub-binary alloys

Experimental data in the literature are almost limited to determine the thermophysical properties of multicomponent complex alloys, especially due to the inability of laboratories to achieve the desired ideal conditions, due to the difficulty of protection from oxidation at high temperatures and other contamination at high temperatures, due to time and cost in laboratory studies. Due to these reasons, the theoretical data obtained in this subject is of great importance. In this study, a series of geometric and physical models, such as Chou’s general solution model (GSM), Muggianu’s Model, Kohler’s Model, Toop’s Model, Hillert’s Model, Guggenheim’s Model, Butler’s Model, Egry’s Model and ideal solution model for quasi-binary alloy system for Section A: Ni_{0.4(1 – x)}Cu_xFe_{0.6(1 – x)}. and Section B: (Ni_xCu_0.2Fe_{0.8 – x}) are used to calculate the surface tension-composition and surface tension-temperature curves of the Cu-Fe-Ni ternary liquid system are plotted. The data for this process is evaluated by means of an extended Redlich-Kister-Muggianu polynomial fit to the experimental values of the surface tensions of the binary liquid alloy systems. The obtained results for these models are also compared with the available data in the literature and relatively good agreements are observed. In addition, the surface segregation having important key factor in determining surface tension of the liquid alloy Ni-Fe-Cu has also been investigated in this work.     

Surface tension modelling of liquid Cd–Sn–Zn alloys

The thermodynamic model in conjunction with Butler equation and the geometric models were used for the surface tension calculation of Cd–Sn–Zn liquid alloys. Good agreement was found between the experimental data for limiting binaries and model calculations performed with Butler model. In the case of ternary alloys, the surface tension variation with Cd content is better reproduced in the case of alloys lying on vertical sections defined by high Sn to Zn molar fraction ratio. The calculated surface tension is in relatively good agreement with the available experimental data. In addition, the surface segregation of liquid ternary Cd–Sn–Zn and constituent binaries has also been calculated.     

Thermophysical properties of Cu–In–Sn liquid Pb-free alloys: viscosity and surface tension

The viscosity of a few Cu–In–Sn liquid alloys has been investigated by a number of geometric (Muggianu, Kohler, Toop) and physical thermodynamic models (Kozlov–Romanov–Petrov, Budai–Benko–Kaptay, Schick et al.) and GSM for the cross section (z/y = 1/3) in Pb-free liquid alloy Cu_x–In_y–Sn_z at 1073 K. Moreover, the surface tensions of the same liquid alloys have been investigated by a number of geometric models and the Butler model for the cross section Cu_x–In_y–Sn_z (z/(y + z) = 0, 0.1, 0.3, 0.5, 0.7, 0.9, 1) at the same temperature. The best agreement of the surface tensions was obtained in the Kohler model for x_Cu = 10 at % and the Butler model for x_Cu = 20 at % and x_Cu = 30 at.%, respectively. The best agreement among chosen geometric and physical models and experiment for these selected sections Cu₈₀In₁₅Sn₅, Cu₇₅In₁₅Sn₁₀, Cu₅₅In₇Sn₃₈, Cu₃₃In₅₀Sn₁₇ and Cu₂₆In₅₅Sn₁₉ at 1073 K was obtained for the Budai–Benkö–Kaptay model.     

Theoretical calculation of surface tension and its temperature coefficient associated with liquid Cu–Ti alloys

In this work, the surface tension of Cu–Ti binary liquid alloys is calculated in the framework of Eyring theory as a function of composition and temperature. It is observed that for all investigated alloys the surface tension can be described by a linear function of the temperature with negative slope, and the temperature coefficient of surface tension decreases as Ti-content of the alloys increases linearly. The obtained theoretical results are compared to the experimental data available in the literature as well as to the theoretical results evaluated by using four models, such as the compound formation model, the quasi-chemical approximation for regular solutions, ideal solution model and Butler model treated in literature frequently.     

Estimation of surface tension for high temperature melts of the binary Ag-X alloys

ABSTRACT

Surface tension is a key property to materials. In this work, the surface tension of the binary alloys Ag-X (Au, Cu, Ce, Bi, Sn, Sb, In, Ni, Y, Pd) is carried out by using Butler Model over enter composition ratio at a certain temperature. According to calculation results, the increasing surface tension of the Ag-X (Cu, Au, Ni, Y, Pd) alloy is accompanied by the composition increases. For Ag-Sn alloy, the surface tension calculated by Butler model is consistent with the experimental result at temperature 1273?K. However, other Ag-X alloys can’t be compared due to the lack of the related experimental data. Although the experimental data about surface tension of the Ag-X alloy are limited, we are possible to make a comparison between the calculated results for the surface tension in this study and the available experimental data. Taken together, the surface tension calculated by Butler model that especially the Ag-Sn alloy are consistent with the experimental results at temperature 1273?K.     

Thermodynamic description of the viscosity of liquid solder alloys with minor Co impurities

Because of the increasing complexity and cost of experiments carried out, the data for the multi-component alloy systems have frequently been obtained by numerical modelling. It is clear that the related calculations require reliable data dealing with the pure components and binary alloy systems. Selecting the reliable data concerning the pure components from the literature, the viscosities for the SAC and (SAC)_1?x Co_x solder alloys have been calculated using different viscosity models (geometric and physical). The viscosity decreases as the amount of tin content increases in the SAC387 alloy while the addition of the cobalt to SAC387 solder results in the increasing of the viscosity. Moreover, by computing the root mean square values between theoretical and experimental viscosities, it can be concluded that the lowest value among all models is that of obtained by Kaptay equation.     

Geometric modelling of viscosity of copper-containing liquid alloys

In this work, viscosities of ternary Au–Ag–Cu and Al–Cu–Si liquid alloys have been calculated as a function of gold, aluminium and copper compositions for the sections Au–Ag–Cu (x_Ag/x_Cu = 0.543 at 1373 K), Al_x(Cu₅₀–Si₅₀)_(1–x) and Cu_x(Al₅₀–Si₅₀)_(1–x) at 1375 K using Chou’s general solution model, Muggianu, Kohler, Toop, Hillert, Budai et al., Kozlov et al., Schick et al. and Kaptay et al. models. The present study finds that a comparison of the predicted values of viscosities associated with the geometric and physical models indicate good mutual agreement. The Muggianu model indicates the best agreement with the results obtained for Au–Ag–Cu and Al_x–Cu₅₀–Si₅₀ alloy systems and the Kaptay et al. model, which is a physical model, indicates the best agreement with the results obtained for Al₅₀–Cu_x–Si₅₀.     

液态Sn-Cu钎料的黏滞性与润湿行为研究

金属熔体的黏度和表面张力都是与液态结构相关的敏感物理性质, 且存在一定的相互关系. 对于微电子封装材料而言, 黏度和表面张力均是影响其工艺性能的重要参量. 本文利用回转振动式高温熔体黏度仪测量了Sn-xCu (x = 0.7, 1.5, 2)钎料熔体在不同温度下的黏度值, 发现在一定温度范围内钎料熔体的黏度值存在突变, 可划分为低温区和高温区. 在各温区内, 黏温关系很好地符合Arrhenius方程, 在此基础上讨论了液态钎料的结构特征和演变规律. 同时, 利用黏度值计算了液态Sn-xCu钎料在相应温度下的表面张力, 并通过Sn-xCu钎料在Cu基板上的润湿铺展实验对计算结果进行验证. 结果显示, 润湿角和扩展率的测试结果与表面张力的计算结果具有很好的一致性, 表明通过熔体黏度值来计算锡基二元无铅钎料合金表面张力并评估其润湿性能的方法是可行的. 关键词： Sn-Cu钎料 黏度 表面张力 润湿性     

Surface tension and density of liquid Sn-Ag alloys

The surface tension and density measurements for Sn-Ag alloys were carried out with the sessile drop method. Seven different compositions were investigated in the range from 0.011 to 0.5 mole fraction of Ag, in a broad range of temperature. With increasing concentrations of Ag, both density and the surface tension are increased. With increasing temperature the density decreases for all of the alloys. A decrease of the surface tension is observed for most of the composition except for the alloy of 0.5 mole fractions of Ag. The obtained results are compared with existing literature data and Butler model calculations and relatively good agreement is observed.     

Ca，Be在镁合金中的阻燃作用

建立了镁合金的晶体,液态及其固/液界面模型.采用递归法计算了Ca,Be在α-Mg、固/液界面、镁液态中的环境敏感镶嵌能,定义并计算了Mg,Ca及Be与氧的原子亲和能.计算结果表明：Ca,Be在镁晶体中的环境敏感镶嵌能较高,不能稳定固溶于晶体中,因此在固体中的溶解度较小.合金凝固时Ca,Be扩散到环境能较低的液体中,向液面聚集.由于Ca,Be与氧的原子亲和能低于镁与氧的亲和能,聚集在液体表面的Ca,Be将优先与氧结合,生成致密的镁与合金元素的混合氧化物,阻止镁合金燃烧. 关键词： 电子结构 阻燃 Mg合金     

Calculation of the surface tension of liquid Ga-based alloys

As known, Eyring and his collaborators have applied the structure theory to the properties of binary liquid mixtures. In this work, the Eyring model has been extended to calculate the surface tension of liquid Ga–Bi, Ga–Sn and Ga–In binary alloys. It was found that the addition of Sn, In and Bi into Ga leads to significant decrease in the surface tension of the three Ga-based alloy systems, especially for that of Ga–Bi alloys. The calculated surface tension values of these alloys exhibit negative deviation from the corresponding ideal mixing isotherms. Moreover, a comparison between the calculated results and corresponding literature data indicates a good agreement.     

An insight into the viscosity prediction of ternary alloys with limited solubility

Geometrical models have been successfully applied into the calculation of viscosity of alloys. However, traditional geometrical (TG) models are feasible only in systems with a complete solubility area. Otherwise, they will not work. In this paper, a new method has been introduced for the calculation of alloy systems with limited solubility. How the new method overcomes the drawbacks of the TG models is discussed and analysed. The viscosity of two alloy systems with limited solubility is calculated by the present model. Comparisons between the experimental viscosity and the calculated values by different models show that our model gives the best results, especially for the data nearby the limited solubility area. The introduction of this model provides a way to solve the calculation problems of ternary alloys with limited solubility, which will extend geometrical models to more practical systems.     

The surface tension and density of the Cu-Ag-In alloys

The surface tension and the densities of the Cu-Ag-In alloys have been measured by means of the sessile drop method. The density of these alloys depends linearly on temperature in the case of all the investigated compositions. The surface tension shows a linear dependence on temperature except for the lowest temperatures. For most of the alloys, the surface tension at the lowest temperature is lower than that predicted by the straight line. The experimental values of the surface tension of the Cu-Ag-In alloys are compared with those computed from the model, and quite good agreement is observed.     

Surface tension and density of liquid Sn-Cu alloys

The surface tension and density of Sn-Cu liquid alloys were measured with the sessile drop method, in a broad range of temperature. Total of seven compositions were investigated in the range from 0.018 to 0.5 mole fraction of Cu. With increasing concentration of Cu, both density and the surface tension are increased. With increasing temperature the density decreases linearly for all of the compositions. The surface tension exhibits similar behavior for most of the compositions, except for the alloy of 0.5 mole fractions of Cu, in which case the increase of the surface tension is observed. The obtained results are compared with existing literature data and Butler model calculations, and a relatively good agreement is observed.     

Surface tension of liquid Cu-Ti binary alloys measured by electromagnetic levitation and thermodynamic modelling

The surface tension of liquid Cu-Ti alloys has been measured by using the containerless technique of electromagnetic levitation and theoretically calculated in the framework of the compound formation model. Measurements have been carried out on alloys covering the entire range of composition and over the temperature range 1275-2050 K. For all investigated alloys the surface tension can be described by a linear function of the temperature with negative slope.Due to the presence of different intermetallic compounds in the solid state the surface properties of liquid Cu-Ti alloys are satisfactory described by the compound formation model.     

Prediction of thermodynamic and surface properties of Pb−Hg liquid alloys at different temperatures

The thermodynamic properties, such as free energy of mixing, heat of mixing, activity and structural properties, such as concentration fluctuation in long wavelength limit, short-range order parameter of Pb–Hg liquid alloy at 600 K have been calculated using theoretical modelling. It has then been correlated with modified Butler model to compute the surface tension of the alloys at different temperatures. The Pb–Hg system at 600 K is found to be ordering at higher concentration of Pb.     

Thermophysical properties of undercooled liquid Co-Mo alloys

Using electromagnetic levitation in combination with the oscillating drop technique and drop calorimeter method, the surface tensions and specific heats of undercooled liquid Co-10 wt% Mo, Co-26.3 wt% Mo, and Co-37.6 wt% Mo alloys were measured. The containerless state during levitation produces substantial undercoolings up to 223 K (0.13 T _L), 213 K (0.13 T _L) and 110 K (0.07 T _L) respectively for these three alloys. In their respective undercooling ranges, the surface tensions were determined to be 1895 m0.31(T m1744), 1932 m0.33(T m1682), and 1989 m0.34(T m1607) mN m^?1. According to the Butler equation, the surface tensions of these three Co-Mo alloys were also calculated, and the results agree well with the experimental data. The specific heats of these three alloys are determined to be 41.85, 43.75 and 44.92 J mol^?1 K^?1. Based on the determined surface tensions and specific heats, the changes in thermodynamics functions such as enthalpy, entropy and Gibbs free energy are predicted. Furthermore, the crystal nucleation, dendrite growth and Marangoni convection of undercooled Co-Mo alloys are investigated in the light of these measured thermophysical properties.     

Thermodynamic and surface properties of Sb-Sn and In-Sn liquid alloys

The thermodynamic properties of Sb-Sn and In-Sn liquid alloys have been studied using the quasi-chemical model for compound forming binary alloys and that for simple regular alloys. The concentration fluctuation S _cc(0) and the Warren-Cowley short-range order parameter (α ₁) were determined for the whole concentration range at a temperature of 770 K. The surface tensions of these liquid alloys were determined for the whole concentration range by using energetics determined from thermodynamic calculations. In all calculations, In-Sn manifested properties very close to alloys of ideal mixing, while Sb-Sn showed properties that are asymmetric about equiatomic composition. Our results suggest that a weak complex of the form SbSn₂ could be present in the Sb-Sn alloy at a temperature of about 770 K.     

The surface tension of liquid Cu-Fe-Sb alloys

The results of study on the influence of temperature and iron and antimony on the surface tension of liquid ternary Cu-Fe-Sb systems are presented. The measurements were carried out with the sessile drop method, in a broad range of the alloy additions concentration (Fe and Sb). It was demonstrated that the surface tension varies as a linear function of temperature and concentration of iron. It was also demonstrated that antimony, in examined alloys, shows the properties characteristic of a surface-active substance, significantly reducing the surface tension value. The changes of the surface tensions as a function of concentration of antimony were described with the Szyszkowski's equation. Composition of surface layer, enriched with an antimony, was determined basing on the model, which used data regarding properties of binary systems. The surface tension values of Cu-Fe-Sb systems was also computed from model and compared with experimental data. A good agreement was obtained.