Non-spherical Ions
The concept of ionic radii is based on the assumption of a spherical ion shape. However, from a group-theoretical point of view the assumption is only justified for ions that reside on high-symmetry crystal lattice sites like Na and Cl in halite or Zn and S in sphalerite. A clear distinction can be made, when the point symmetry group of the respective lattice site is considered, which are the cubic groups Oh and Td in NaCl and ZnS. For ions on lower-symmetry sites significant deviations of their electron density from a spherical shape may occur. This holds in particular for ions on lattice sites of polar symmetry, which are the crystallographic point groups C1, C1h, Cn or Cnv, n = 2, 3, 4 or 6. A thorough analysis of the bonding geometry was recently carried out for pyrite-type disulfides, where monovalent sulfur ions reside on C3 lattice sites. It was found that the sulfur ions have to be modeled by thermal ellipsoids with different radii in direction of the symmetry axis and perpendicular to it. Remarkably, it turned out in this case that it is not the ionic radius, but the ionic volume that remains constant in different crystalline compounds.
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