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A density functional study of vacancy formation in grain boundaries of undoped a-alumina,  T. Ogawa, A. Kuwabara, C. A. J. Fisher, H. Moriwakea, K. Matsunaga, K. Tsuruta, S. Kitaoka,   Acta Mater, 69 , 365-371{https://www.sciencedirect.com/science/article/pii/S1359645414000810}, May 2014


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