Crystal co-ordination of the barium ion

A systematic study has been made of the crystal co-ordination of the barium ion in various compounds whose structures have been solved. Apart from the more common co-ordination polyhedra which are enumerated in text-books, a number of new polyhedra have been identified, particularly in cases where the co-ordination numbers are unusual, such as ten or eleven. According to the radius-ratio rule of Pauling, a co-ordination number of nine or ten is normally expected for the barium ion. The present investigations, however, reveal that it shows a variety of co-ordinations with ligancies from six up to twelve. Some of the factors that might possibly enter in explaining this wide range of co-ordination numbers are discussed. It appears as though the part played by the Ba2+ ion in deciding the structure is secondary, limiting itself only to occupying vacant spaces provided by other atoms in the crystal.

Nonclassical Paths in Quantum Interference Experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.