Behaviors of diffusion induced grain-boundary migration (DIGM) in ZST ceramics which have been used as mic-rowave dielectrics were investigated as a function of heat treatment temperature. The specimens were sintered for 2h at 140$0^{circ}C$ with the addition of 1-9wt% La2O3 when the specimens were het-treated in SnO2 atmosphere at 135$0^{circ}C$ the grain-boundaries migrated away from their centers of curvature leaving behind an SnO2 rich solid solution. On the contrary when the specimens were heat-treated in SnO2 atmsophere at 140$0^{circ}C$ DIGM did not occur. The coherency breaking at thin diffusion zone ahead of the migrating grain-boundary be expected to occur due to fast bulk diffusion at high temperature