Structural origin of Sn–Bi–Zn ternary eutectic: A cluster model perspective with experimental validation

Sn-based ternary eutectics are important solders for electronic packaging owing to their low melting point, good fluidity, and weld ability. However, it is difficult to accurately determine a ternary eutectic point by experiments, as exemplified by the Sn–Bi–Zn ternary eutectic solder covering a quite broad range of Sn 54∼57 Bi 39∼41 Zn 2∼6.25 . In this work, this eutectic is analyzed both following the cluster formula approach and by experimental verification. Our theoretical approach is based on the cluster-plus-glue-atom (CPGA) model, which identifies the chemical unit of any structure covering only a nearest-neighbor cluster plus a few next-neighbor “glue” atoms, expressed as cluster formula of [cluster](glue atoms). Assuming that a ternary eutectic is composed of two binary ones (whose formulas are previously known) sharing a common “solvent unit” of Sn, this eutectic is formulated as 6{[Sn–Sn 10 ]Sn 5 }+6{[Bi–Bi 6 ]Bi 5 }+[Zn–Zn 12 ]Zn 3 = 6{Sn 16 }+ 6{Bi 12 }+{Zn 16 } = Sn 52.17 Bi 39.13 Zn 8.70 , where {Sn 16 }+{Bi 12 } = Sn 57.1 Bi 42.9 and 6{Sn 16 }+{Zn 16 } = Sn 85.7 Zn 14.3 respectively represent the two binary eutectics in Sn–Bi and Sn–Zn systems. This theoretic estimation deviates largely from any reported eutectic points. Experiments are then conducted for the verification. Differential scanning calorimetry and XRD results indicate that the formulated composition exhibits a single melting or solidification peak while the reported eutectic points all show an additional minor peak. Our work provides an important theoretical basis for accurately determining ternary eutectic compositions, from which new multi-component Sn-based solders can be obtained.