Sn-Bi Alloys Research Articles

Study on the Influence of Casing Surface Morphology on the Plugging Performance of Downhole CO2 Plugging with Sn58Bi

Aimed at the problem of gas flurries in carbon dioxide (CO2) geologic sequestration in the wellbore, this paper proposes a sealing method in which the downhole casing is processed with threaded grooves and then plugged with a low-melting-point alloy plug. Based on this method, a small-scale experimental setup was developed for alloy plug molding and gas sealing in this study. Molding and gas sealing experiments with Sn58Bi alloy plugs inside casings with different surface morphologies were carried out. The gas leakage pathway was determined. The microstructure of the interface between the alloy plug and casing was analyzed using an optical microscope. The influence of the inner surface roughness, threaded groove, length-to-diameter ratio, and ambient temperature on the gas sealing performance of the alloy plugs was analyzed. The experimental results show that, with an increase in ambient temperature, the gas sealing performance of the casing increases significantly; when the inner surface of the casing is processed through threaded grooves, the gas sealing performance is better than with smooth hole casing; the gas sealing performance of the alloy plug presents an obvious linear positive correlation with their length-to-diameter ratio. This research provides theoretical support for downhole CO2 plugging using Sn58Bi in the casing.

Enhancing Magnesium-Ion Storage in a Bi-Sn Anode through Dual-Phase Engineering.

Magnesium-ion batteries (MIBs) are a "beyond Li-ion" technology that are hampered by Mg metal reactivity, which motivates the development of anode materials such as tin (Sn) with high theoretical capacity (903 mAh g-1). However, pure Sn is inactive for Mg2+ storage. Herein, Mg alloying with Sn is enabled within dual-phase Bi-Sn anodes, where the optimal composition (Bi66.5Sn33.5) outperformed single-phase Bi and Sn electrodes to deliver high specific capacity (462 mAh g-1 at 100 mA g-1), good cycle life (84% after 200 cycles), and significantly improved rate capability (403 mAh g-1 at 1000 mA g-1). Density functional theory (DFT) calculations revealed that Mg alloys first with Bi and the subsequent formation of the Mg3Bi2//Sn interfaces is energetically more favorable compared to the individual Mg3Bi2 and Sn phases. Mg insertion into Sn is facilitated when Mg3Bi2 is present. Moreover, dealloying Mg from Mg3Bi2:Mg2Sn systems requires the creation of Mg vacancies and subsequent Mg diffusion. Mg vacancy creation is easier for Mg2Sn compared to Mg3Bi2, while the latter has slightly lower activated Mg-diffusion pathways. The computational findings point toward easier magnesiation/demagnesiation for BiSn alloys over pure Bi or pure Sn, corroborating the superior Mg storage performance of Bi-Sn electrodes over the corresponding single-phase electrodes.

The Effect of In Concentration and Temperature on Dissolution and Precipitation in Sn-Bi Alloys.

Sn-Bi-based, low-temperature solder alloys are being developed to offer the electronics manufacturing industry a path to lower temperature processes. A critical challenge is the significant microstructural and lattice parameter changes that these alloys undergo at typical service temperatures, largely due to the variable solubility of Bi during the Sn phase. The influence of alloying additions in improving the performance of these alloys is the subject of much research. This study aims to enhance the understanding of how alloying with In influences these properties, which are crucial for improving the alloy's reliability. Using in situ heating synchrotron powder X-ray diffraction (PXRD), we investigated the Sn-57 wt% Bi-xIn (x = 0, 0.2, 0.5, 1, 3 wt%) alloys during heating and cooling. Our findings reveal that In modifies the microstructure, promoting more homogeneous Bi distribution during thermal cycling. This study not only provides new insights into the dissolution and precipitation behaviour of Bi in Sn-Bi-based alloys, but also demonstrates the potential of In to improve the thermal stability of these alloys. These innovations contribute significantly to advancing the performance and reliability of Sn-Bi-based, low-temperature solder alloys.

Microstructure and shear properties of interconnect interface between multi-phase heterogeneous SnBi eutectic alloy and Cu substrate

The microstructures of the interconnect interfaces between Sn58Bi eutectic alloy and Sn53Bi3Cu3Zn2Ag2Sb multiphase alloy and Cu substrate, as well as the strength of the interconnect joints were systematically studied after 1008 h thermal aging at 70℃. Compared with the unmodified Sn58Bi alloy, the addition of alloying elements inhibited the coarsening of the organization and the growth of intermetallic compound (IMC) at the interconnect interface. At the same time, the Cu3(Sn, Zn) phase in the upper part of the IMC and twinned Cu in the substrate can contribute to enhanced the mechanical properties of the interconnect joints. Compared to their respective shear strengths after reflow, the strength of the modified Sn53Bi3Cu3Zn2Ag2Sb/Cu interconnect joints increased by 22.3 %, while the strength of the Sn58Bi/Cu interconnect joints decreased by 18.3 % after thermal aging. This study indicate that alloying modification can effectively improve the shear strength of interconnect joints during aging, thus improving interconnect reliability.

Evaluation of Solidification and Interfacial Reaction of Sn-Bi and Sn-Bi-In Solder Alloys in Copper and Nickel Interfaces

Although there are studies devoted to lower Indium (In) addition, Sn-Bi alloys containing 10 wt.% In or more have been barely investigated so far. Higher In contents may offer the potential for improved joint production, better control over the growth of interfacial layers, and enhanced mechanical strength. The present article focuses on the solidification, wettability, adhesion strength, and interfacial intermetallic growth in the Sn-40%Bi-10%In alloy soldered on Cu and Ni pads. SEM-EDS, wettability tests, and tensile tests were performed. The contact angles were measured in Cu and Ni as 24° and 26°, respectively. Indium addition promoted coarsening of the as-solidified microstructure due to an increase in the alloy solidification range. The Bi spacing was increased at least three times, with a strong segregation of Bi towards the interface. The formation and growth of alloy/Cu reaction layers were also evaluated under the different aging conditions of the as-soldered joints, simulating real service. A growth kinetics model of the reaction layer showed that In increases the activation energy, thereby reducing the layer growth. The adhesions of the formed intermetallics films in Cu and Ni were analyzed using tensile tests. It was observed that the alloy/Ni couple exhibited better adhesion. Premature fracturing appears to happen in the alloy/Cu joint due to the higher intermetallic compound’s (IMC) thickness, rough morphology, and coarser microstructure. Both ductile fracture features with dimples and cleavage zones associated with Bi, Cu6(Sn,In)5, and Ni3Sn4 intermetallics were observed.

The effect of well temperature on the microstructure and the mechanical performance of bismuth-based plugs in well plugging and abandonment operations

Bismuth-tin (BiSn) alloys are considered promising candidates as potential alternatives to cement for well plugging and abandonment (P&A) applications to prevent any uncontrolled flow of deep reservoir fluids to the surface. As the temperature in the well varies with depth, the final microstructure of the BiSn alloy after its solidification might be influenced, and consequently the mechanical performance of the alloy will also be affected. The aim of this study is to evaluate the microstructural evolution of the BiSn alloy after solidification, at temperatures between 20 °C and 90 °C, to reflect in situ conditions from approximately 800m to 3 km depth. Microstructural characterization was carried out by using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). The microstructural analysis revealed that the plug subjected to the lower temperature resulted in finer microstructure, whereas the grain size of the material was increased at higher temperatures. Additionally, the theoretical lever rule was employed to validate the microstructural findings. The observed microstructures were also correlated with tensile tests, which showed that the plug at 20 oC had a yield strength of 67,25 MPa, whereas the yield strength of the plug at 90 oC was only 41,64 MPa. In addition, hydraulic push-out tests further confirmed that lower testing temperatures correlate with higher pressure tolerance of the plug. The plug at 20 oC could withstand 113,5 bar, compared to the plugs at 60 oC and 90 oC which could withstand 90,4 and 50,9 bar, respectively. From all the experimental tests conducted, the outcome was that the lower temperature of 20 oC resulted in a material with a finer microstructure, which plays an important role in enhancing the mechanical properties of the bismuth-based plug. This study aims to advance the understanding of BiSn alloy performance in plug and abandonment (P&A) operations, thereby supporting the industry's efforts to qualify BiSn alloys as effective well-barrier materials.

Investigation of the mechanical properties of lead-free Sn-58Bi solder alloy with cobalt addition through flux doping

PurposeThis study aims to investigate the effect of incorporating cobalt (Co) into Sn-58Bi alloy on its phase composition, tensile properties, hardness and thermal aging performances. The fracture morphologies of tensile-tested solders are also investigated to correlate the microstructural changes with tensile properties of the solder alloys. Then, the thermal aging performances of the solder alloys are investigated in terms of their intermetallic compound (IMC) layer morphology and thickness.Design/methodology/approachThe Sn-58Bi and Sn-58Bi-xCo, where x = 1.0, 1.5 and 2.0 Wt.%, were prepared using the flux doping technique. X-ray diffraction (XRD) is used to study the phase composition of the solder alloys, whereas scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) are used to investigate the microstructure, fractography and compositions of the solders. Tensile properties such as ultimate tensile strength (UTS), Young’s modulus and elongation are tested using the tensile test, whereas the microhardness value is gained from the micro-Vickers hardness test. The morphology and thickness of the IMC layer at the solder’s joints are investigated by varying the thermally aging duration up to 56 days at 80°C.FindingsXRD analysis shows the presence of Co3Sn2 phase and confirms that Co was successfully incorporated via the flux doping technique. The microstructure of all Sn-58Bi-xCo solders did not differ significantly from Sn-58Bi solders. Sn-58Bi-2.0Co solder exhibited optimum properties among all compositions, with the highest UTS (87.89 ± 2.55 MPa) at 0.01 s−1 strain rate and the lowest IMC layer thickness at the interface after being thermally aged for 56 days (3.84 ± 0.67 µm).Originality/valueThe originality and value of this research lie in its novel exploration of the flux doping technique to introduce minor alloying of Co into Sn-58Bi solder alloys, providing new insights into enhancing the properties and performance of these solders. This new Sn-Bi-Co alloy has the potential to replace lead-containing solder alloy in low-temperature soldering.

Effects of Different Zinc Content on Solidification, Microstructure, and Mechanical Properties in Tin–Bismuth Alloy

The present aims to evaluate the effect of adding Zn (0.5% and 9.0% in wt%) on phase transformation temperatures, microstructure coarsening, solidification parameters (cooling rate‐L and growth rate‐VL), macrosegregation, and mechanical properties of directionally solidified Sn‐34wt%Bi‐xZn alloys. The samples have been characterized by optical microscopy, scanning electron microscopy, X‐ray fluorescence, and X‐ray diffraction, in addition to Vickers microhardness and tensile tests. The CALPHAD method has been used for thermodynamic computations via Thermo‐calc software, in order to obtain thermodynamic data. The microstructure of Sn–Bi–Zn alloys is mainly dendritic, composed of a Sn‐rich matrix (β‐Sn) with Bi precipitates inside and surrounded by a Sn+Bi eutectic mixture of phases, predominantly observed at the coarse scale. Coarse Zn needles are also observed in the Sn‐34wt%Bi‐9wt%Zn alloy due to the high Zn content. On the whole, Zn provoked a coarsening of the dendritic arrangement. Moreover, Zn additions cause inverse segregation of Bi, as compared to the rather constant macrosegregation profile observed in the binary Sn–Bi alloy. On the whole, both additions of Zn (0.5 and 9.0) promoted increase in Vickers microhardness, yield strength (σY), and ultimate tensile strength (σu), however, causing an overall reduction in elongation‐to‐fracture (δ).

Investigating into casting LMPA (low-melting-point alloy) with 3D-printed mould and inspecting quality using 3D scanning

PurposeThree-dimensional (3D) casting means using additive manufacturing (AM) techniques to print the mould for casting the cast tool. The printed mould, however, should be checked for its dimensional accuracy. 3D scanning can be used for the same. The purpose of this study is to combine the different AM techniques for 3D casting with 3D scanning to produce parts with close tolerance for preparing electrical discharge machining (EDM) electrodes.Design/methodology/approachThe four processes, namely, stereolithography, selective laser sintering, fused deposition modelling and vacuum casting, are used to print the casting mould. The mould is designed in two halves, assembled to form a complete mould. The mould is 3D scanned in two stages: before and after using it as a casting mould. The mould's average and maximum dimensional deviations are calculated using 3D-scanned results. The eutectic Sn-Bi alloy is cast in the mould. The surface roughness of the mould and the cast tool are measured.FindingsThe cast tool is selected from the four processes in terms of dimensional accuracy and surface finish. The same is electroplated with copper. The microstructure of the cast tool (low-melting-point alloy) and deposited copper is analysed using a scanning electron microscope. Energy dispersive spectroscopy and X-ray diffraction techniques are used to verify the composition of the cast and coated alloy. The electroplated tool is finally tested on the EDM setup. The material removal rate and tool wear are measured. The performance is compared with a solid copper tool. The free-form customised EDM mould is also prepared, and the profile is cast out. The same is tested on the EDM. Thus, the developed path can be successfully used for rapid tooling applications.Originality/valueThe eutectic composition of Sn-Bi is cast in the 3D-printed mould using different AM techniques combined with 3D scanning quality to check its feasibility as an EDM electrode, which is a novel work and has not been done previously.

All-electrochemical synthesis of SnBi/SnAgCu structures for low-temperature formation of high-reliability solder microjoints

There is a growing interest in low temperature soldering, yet the use of low-melting point alloys for interconnection is often hindered by reliability concerns. Eutectic tin-bismuth (SnBi) alloy is being considered for soldering to Sn3Ag0.5Cu (SAC305) bumps at lower temperatures (150 °C), but the resulting hybrid structures are not very reliable. We have recently shown that superior reliability can be achieved by a post-soldering anneal to distribute up to 6 % Bi throughout the joint. However, the new approach is impractical for solder joints taller than 70 µm and the manufacturing feasibility in such cases warrants both SnBi and SAC305 to be electroplated. The present study utilizes electrochemistry to broaden the applicability of the aforementioned approach by the development of optimized routines for the separate electroplating of both structural alloys. The synthesis of the SAC305 alloy employs elemental co-deposition under strict thickness control, and the SnBi eutectic mixture may be produced likewise and deposited atop to enable low-temperature soldering. If the SnBi is deposited on separate pads, better composition control may be achieved alternatively by the successive plating of both metals, followed by reflow to facilitate their mixing. The established plating routines are further fine-tuned for the processing of an array of pillars.

Fabrication and characterization of Sn-57 wt% Bi film by pulse DC current co-electrodeposition and reflow

The electrodeposited Sn-Bi eutectic alloys can satisfy the need for micro-bumps with low melting point in 3D packaging. We deposited Sn-Bi film by pulse DC current in electroplating solutions based on methane sulfonic acid (MSA). The effects of MSA concentrations and pulse frequencies on morphology and composition of deposits were investigated. As the MSA concentration increased from 120 ml/L to 160 ml/L, the hydrogen evolution reaction weakened resulting in smoother deposited surfaces, and the Bi content decreased. In the use of pulses allowing deposits to become more uniform and denser, the Sn-56.73 wt% Bi film with smooth surfaces were fabricated at a pulse frequency of 4 Hz and an MSA concentration of 120 ml/L, of which melting point was 134.35 °C. By using transmission electron microscopy (TEM) and electron backscattered diffraction (EBSD), the structures were characterized more microscopically, which are essential for diffusion and electromigration of micro-bumps. The near-eutectic deposits, both before and after reflowing, consisted of uniformly distributed tetragonal β-Sn phases and hexagonal Bi phases, and the most preferred orientations after reflowing were the same as before reflowing, that were (220)//ND for β-Sn and (1̅012)//ND for Bi. The average grain sizes of Sn and Bi in the deposits after reflowing were 1.44 µm and 0.64 µm, respectively, which were much smaller than those of Sn58Bi alloy obtained by rapid solidification. Dislocations were observed in Sn grains and misorientation values in β-Sn phases were larger, which illustrated that the β-Sn phase carried larger strains. As evaluated by constant loading rate (CLR) nanoindentation tests, the hardness and modulus were significantly improved after reflowing, and creep stress indices of the deposits before and after reflowing were 51.74 and 7.07, respectively.

Effect of Sb and Ag Addition and Aging on the Microstructural Evolution, IMC Layer Growth, and Mechanical Properties of Near-Eutectic Sn-Bi Alloys

Effect of Sb and Ag Addition and Aging on the Microstructural Evolution, IMC Layer Growth, and Mechanical Properties of Near-Eutectic Sn-Bi Alloys

SnBi Alloy Composites Via Controlling Cooling Rate for High Performance Lithium-Ion Battery Anode

Alloying-based materials, such as tin (Sn) and bismuth (Bi), have been considered as potential anode materials for lithium-ion batteries (LIBs) due to their high theoretical volumetric capacities of 1991 and 3765 mAh cm−3, respectively. However, these materials tend to have short cycle lives due to severe volume expansion when fully lithiated, such as Li4.4Sn (300%) and Li3Bi (215%), which presents a great challenge for practical implementation. To address this issue, using two metal alloys is an effective strategy to improve electrode integrity and stability. The different working voltages of Bi (0.78−0.69V) and Sn (0.65−0.1V) hinder the extreme structural changes that occur upon cycling. At the initial discharge stage, the unreacted Sn phase acts as a buffer during the lithiation of Bi. Meanwhile, the lithiated state of Bi (LixBi) will buffer the expansion when Sn is lithiated with Li-ions. However, the definition and mechanism of the buffer effect between active-active metals are still unclear. As a result, the bismuth-tin (BiSn) alloy is designed through heat treatment by controlling the cooling rate to form micro-phase alloys (BiSnM) and nano-phase alloys (BiSnN). The BiSn nano-phase alloy anode (BiSnN) exhibits a better buffer effect and achieves a superior discharge capacity of 550 mAh g−1 at 0.1 A g−1 and 320 mAh g−1 at 2 A g−1.

Investigating the Effects of Rapid Precipitation of Bi in Sn on the Shear Strength of BGA Sn-Bi Alloys

Investigating the Effects of Rapid Precipitation of Bi in Sn on the Shear Strength of BGA Sn-Bi Alloys

The Effect of Temperature on the Electrical Resistivity of Sn-Bi Alloys

The Effect of Temperature on the Electrical Resistivity of Sn-Bi Alloys

In-situ investigation of the time-temperature dependent lattice and microstructure of Sn-Bi alloys

Alloys based on the Sn-Bi system are widely considered as the most promising candidates for low temperature solders (LTS) in the electronics industry due to their low liquidus temperature, non-toxicity and relatively low cost. However, implementation of LTS is complicated as they exhibit different characteristics from conventional Pb-free solders. While the solid solubility of alloying additions in Sn is typically <1 wt% in the current generation of Pb-free solders, the solubility of Bi in Sn ranges from less than 3 wt% at room temperature to 21 wt% at the eutectic temperature of 139 °C. In consequence, the microstructure and properties of Sn-Bi solders change significantly under varying temperature during normal service, affecting reliability. Since these changes are time and temperature dependent, interpreting results obtained using ex-situ methods requires assumptions about the stability of the alloy during transitions from the test environment to the observation environment, leading to an incomplete understanding of these changes. To address this, in-situ synchrotron powder X-ray diffraction (PXRD) and in-situ scanning electron microscopy (SEM) techniques were developed to investigate the time-temperature dependent lattice and microstructure of hypo-eutectic Sn-37wt%Bi and near-eutectic Sn-57wt%Bi solder alloys. This made possible for the first time the observation of changes during temperature fluctuations. The study revealed that lattice and microstructure are highly sensitive to factors like temperature ramp rate and isothermal holding time, not previously considered. The results will impact the design of electronic circuitry and process parameters during electronics assembly to enhance reliability and performance.

Impact reliability enhancement approach of Sn–Bi–Zn–in alloy bumps under high-humidity and high-temperature tests

Sn–45Bi–2.6Zn–0.5In and Sn–45Bi–2.6Zn–1In alloys have previously been shown to be superior to Sn–58Bi under the thermal aging test. In this study, a comparative analysis of the microstructure and impact strength of Sn–58Bi, Sn–45Bi–2.6Zn–0.5In, and Sn–45Bi–2.6Zn–1In alloy bumps was conducted before and after high-humidity and high-temperature tests. Cross-sectional microstructure observations and impact tests were performed on all alloy bumps. The results indicated that the high-humidity and high-temperature conditions had a slight influence on the Sn–58Bi alloy bump, but it reduced the maximum force of Sn–45Bi–2.6Zn–0.5In and Sn–45Bi–2.6Zn–1In to almost zero and generated voids at the interface between the alloy and Cu pad after the test. This deterioration was mainly attributed to the formation of voids on the accumulated Zn at the interface under the effects of both high-humidity and high-temperature conditions. In addition, a possible approach for enhancing the impact strength of Zn-containing alloy bumps by adjusting the heating profile was proposed, and it was verified that the maximum force of the Zn-containing alloy bumps was significantly improved.

Properties of Mixing SAC Solder Alloys with Bismuth-Containing Solder Alloys for a Low Reflow Temperature Process

The subject of extensive research has been the establishing of lower temperature soldering of electronic assemblies that are similar to the once common yet still preferred eutectic Tin-Lead (SnPb) soldering processes that are below 217˚C. This research measured and compared the mixing mechanisms of paste and ball dissolution. Mixed soldered assemblies will have different dissolution results that are dependent on the peak reflow temperature. The hypothesis for this experiment was to determine the relationship of various times above the melting point of low temperature solders containing Bismuth. The results measured are from solder joints of both SAC305 and Bismuth containing solders formed at lower process temperatures compared to the standard high temperatures which peak at 230˚C-260˚C. The Bismuth containing solders evaluated start with the highest to lowest weight percentage of Bismuth, the eutectic 58Bismuth/42Tin (58Bi/42Sn), 57Bi/42Sn/1Ag and a propriety alloy that has a lower Bismuth content along with various micro alloys, defined as 40-58Bi/Sn/X (X representing proprietary micro alloys or doping). The assembly was with an 18mil 96.5Tin/3.0Silver/0.5Copper (SAC305) solder ball mixed with each solder paste. These solder alloys were exposed to three different peak temperatures 180˚C, 195˚C, 205˚C. Another reflow profile attribute of focus was times above 138˚C - the melting point of the eutectic Sn58Bi alloy, this term used throughout the study is referred to Time Above Melting (TAM). The ball and paste assembly used the times above melting of 120sec and 240sec to represent process extremes and verify their significance on improving mixing level results. The average mixing % levels were recorded and compared for each solder joint combination to test the theory that the solder paste solidifies during the time above melting (TAM) within the reflow oven. [1] This experiment effectively demonstrates that the reflow profile parameter for time above melting has limited effectiveness in additionally mixing the paste with the BGA solder ball. Optimization of mixing percentages will need to be achieved by optimizing the paste and ball volumes.

Comprehensive analysis of Sn58Bi/Cu solder joints reinforced with Mg particles: Wettability, thermal, mechanics, and microstructural characterization

In this study, the Sn58Bi-xMg (x = 0, 0.2, 0.4, 0.6, 0.8, 1.0) composite solders were synthesized to explore the impact of Mg particles. The study examined the wettability, thermal properties, mechanical properties, microstructure, and growth of interfacial IMC (intermetallic compound) of composite solder. Experimental results showed that adding Mg particles had no significant impact on the melting point of Sn58Bi solder. However, increasing the Mg content increased the undercooling of the solder. Moreover, the incorporation of Mg particles resulted in a consistent rise in the coefficient of thermal expansion (CTE) of the composite solder, ranging from 11.4 × 10−6/°C to 15.6 × 10−6/°C. It was worth noting that including Mg particles enhanced the wetting ability of Sn58Bi alloy on Cu substrates. With a 0.4 % addition of Mg particles, the wetting area could be increased by 60.14 %, and the lowest wetting angle was approximately 10.43°. Adding Mg particles resulted in an amelioration in the brittleness of the Bi-rich phase within the solder matrix, coupled with a decrease in both the thickness of IMC and the grain size at the joint interface. Compared to the joints without mixed Mg particles, the shear strength of Sn58Bi-0.4Mg solder joints and the microhardness of the alloy increased by 30 % and decreased by 10 %, respectively. Also, the presence of dimples within the fracture indicated a rise in the ductility of the solder joints. Overall, adding 0.4 wt% Mg particles in this experiment resulted in a more effective modification of the Sn58Bi solder comprehensive properties.

An analytical model for calculating tie-line critical temperature in ternary immiscible alloys

An analytical model for calculating the tie-line critical temperature (TtC) in ternary immiscible alloys is proposed in this study. The results of the TtC for Al–Pb–Sn and Al–Bi–Sn alloys calculated by using the proposed model show a favorable agreement with the results obtained from the CALPHAD method and the experimental data, which verifies the correctness of the model. Based on the proposed model, the tie-line critical temperatures of several alloy systems, such as Al–In–Pb and Al–Bi–Pb, are calculated. The characteristics of the tie-lines in the ternary immiscible system are analyzed and discussed. The results indicate that ternary immiscible alloys can be divided into two types according to their characteristics of the tie-lines. For type I, the tie-line is nearly parallel to the edge binary system. For type II, there is a certain or large angle between the tie-line and the edge binary system. The relationship between the parameters for representing the tie-line equation and the critical point composition (xC) is determined by fitting the linear and secondary polynomial functions.