Polycrystalline aluminum oxide has been used to realize a higher luminance for the arc tubes of metal-halide lamps. However, cracks occasionally develop inside the glass frit used for sealing. The microstructures of samples, which were sealed by annealing during the cooling step of the sealing process, were investigated at the interface between the Al2O3 capillary and the glass frit. The Al2O3 grains remain semi-separated from the inner surface of the Al2O3 capillary. Consequently, Al2O3 crystal grains grew anisotropically in the radial direction of the seal by annealing during the cooling step of the sealing process. The number of crystals grains decreased continuously with the distance from the Al2O3 capillary, and a composition gradient was present with regard to the Al2O3 crystal grains. In other words, the sealing stress is also relaxed when the CTE gradually changes at the sealing interface. Therefore, the formation of cracks inside the glass frit in the axial direction of the Al2O3 capillary can be prevented by the growth of Al2O3 crystal grains.