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Application of the LCAO method for energy band calculation in nanocrystals

Simanta Hazarika, Hira Lal Das, Anurup Gohain Barua

On the basis of the LCAO method, the energy band width of a conduction electron in a one dimensional crystal is found to be 4ã. The quantity ã is a measure of overlapping interactions among the atomic orbitals of a conduction electron. In the present work, this method is applied to a copper (f.c.c.) nanocrystal of size equal to 10a (a being the lattice constant) to see the nature of dependence of ã on the nanocrystal size. It is found that ã increases inversely as the size of nanocrystals. This agrees well with the observation that the energy band widths in nanocrystals are wider compared to those of the corresponding bulk materials.