**Acknowledgements**

The authors thank to Mr. Masakazu Kawahara (Fuji Electric Industry Co. Ltd.) and Mr. Shinichi Takei (SinterLand Inc.) for useful discussion and Mr. Huu Hien Nguyen who is a graduate student of Nagaoka University of Technology, for conducting experiments on colored Al2O3 and MgAl2O4 and observation of black dots in transparent polycrystalline Al2O3.
