Phase field modeling of grain boundary migration and preferential grain growth driven by electric current stressing

Abstract

A phase field model incorporating the electrostatic free energy and the grain orientation effect is developed and employed to study the grain boundary migration and preferential grain growth in widely used beta-tin (β-Sn) under electric current stressing. The directional migration of grain boundaries and the preferential growth of the grain with its orientation having low electrical resistivity along the electric current direction are theoretically clarified. In a bicrystal system containing a circular grain, the shrinkage velocity and morphology changes of grains are dominated by the competition effect between the grain boundary energy and the electrostatic free energy; in particular, the high-density electric current can induce the instability of grain morphology evolution. Moreover, grain morphology evolution leads to the change of the voltage across the β-Sn system; it is found that the voltage decreases over time in a tricrystal system, while the variation of the voltage across the bicrystal system is related to the above-mentioned competition effect. The proposed model and results provide insights into the orientation-related microstructure evolution under electric current stressing.