Non-Equilibrium Thermodynamic Theory of 4-Component Lead-Free Solder

Abstract

We investigated non-equilibrium thermodynamic theories for 4-component lead-free solders based on classical thermodynamics using one-dimensional oscillator model to obtain their specific heat and the coefficient of linear thermal expansion. We analyzed In and Sn reactions in SnAgBiIn solder as a representative lead-free material and experimentally obtained an Nc factor for expressing the state of non-equilibrium from the formation of metallic compounds. It was considered that the state of equilibrium did not occur experimentally, and that metallic compounds InSn4 formed in some parts of the 2-component eutectic solder. We then built a theory as onedimensional oscillator model by approximating this Nc factor, as a representation of the non-equilibrium behavior of high temperature lead-free solder. Using this model representing the non-equilibrium state, the correlation between specific heat and coefficient of linear thermal expansion was derived theoretically, which was found to be linear in mathematical studies. In fact, it was learned that experimental results of this correlation also tended to be linear. This suggested that the derived non-equilibrium theory was practically useful, moreover other thermodynamic characteristics could be analyzed by this non-equilibrium thermodynamic theory using one-dimensional oscillator model.