Complex changes in the framework of endohedrally Na-doped type II Si clathrates with respect to Na content

Crystal structures of endohedrally Na-doped type II silicon clathrates with variable Na content were refined by Rietveld analysis. Type II Si clathrates have two types of cages: small and large. The large cages were preferentially occupied by Na atoms. Upon occupation by Na in the large cages, the lattice constant of the clathrates decreased slightly. The attractive interaction of the Na atoms in the large cages with a framework that caused displacement of the Na atoms from the center might influence lattice shrinkage. Moreover, in the region where almost large cages contained Na atoms and the small cages were partially occupied by Na, the lattice constant increased with the Na content; however, the relationship between these features was complex. The lattice constant demonstrated a linear relationship with the size of the small cages; however, the enlargement of the small cages was not linear with respect to its Na occupancy, resulting in complex changes in the lattice constant with respect to the Na content. It was inferred that enlargement of the small cages by Na insertion may be dependent on the Na occupancy of neighboring small cages.