Crystal lattice expansion of nanocrystalline materials

Nanocrystalline materials are characterized structurally by ultra-fine crys tallites separated by grain boundaries. The structure of nanocrystallites s hows significant differences in comparison to perfect crystals. A model is proposed to account for the effects of the defects in the grain boundaries of nanocrystalline materials on the crystal lattice, based on the fact that the grain boundaries of nanocrystalline materials contain a large number o f vacancies and vacancy clusters. A 1/x(3) law for the stress field caused by the vacancies and the vacancy clusters is considered, and the crystal la ttice expansion of nanocrystalline materials is estimated. The theoretical results can interpret experimental observations well. (C) 1999 Elsevier Sci ence S.A. All rights reserved.