Theoretical prediction of thermodynamic activities of all components in the Bi-Sb-Sn ternary lead-free solder system and Pb-Bi-Sb-Sn quaternary system

• Molecular interaction volume model used to predict the thermodynamic activities.
• Activity of Sb in Bi-Sb-Sn shows negative deviation from Raoult's law (ideality).
• Activities of Bi and Sn in Bi-Sb-Sn show transformation of deviation from ideality.
• The activity of Sn in Bi-Sb-Sn system shows feature hidden in published work.
• The activities of all components in Pb-Bi-Sb-Sn system successfully predicted.

Thermodynamic activity of Sn in the ternary lead-free solder, Bi-Sb-Sn has been predicted at 900 K using molecular interaction volume model (MIVM). The results obtained have good agreement with available experimental data. On this premise, we predicted the activities of all components in Bi-Sb-Sn in three cross-sections from the corner of each metal with molar ratio of the other two components being 1:3, 1:1 and 3:1 in the range 500–1000 K. We found that the activities of Bi and Sn show a transformation of negative deviation from Raoult's law to positive deviation while the activity of Sb shows negative deviation from Raoult's law. We also found out that increase in temperature decreases the deviation of activity from Raoult's law in each of the three components of Bi-Sb-Sn and that temperature determines the extent of transformation of deviation from Raoult's law in Bi. The activities of all components in Pb-Bi-Sb-Sn at 700 K were also predicted.