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The radius ratio rule defines a critical radius ratio for different crystal structures, based on their coordination geometry. [1] The idea is that the anions and cations can be treated as incompressible spheres, meaning the crystal structure can be seen as a kind of unequal sphere packing .
An octahedron may then form with a radius ratio greater than or equal to 0.414, but as the ratio rises above 0.732, a cubic geometry becomes more stable. This explains why Na + in NaCl with a radius ratio of 0.55 has octahedral coordination, whereas Cs + in CsCl with a radius ratio of 0.93 has cubic coordination.
Ionic radius, r ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice .
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According to the radius ratio rule, this structure is more likely to be formed if the cation is somewhat smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732). The interatomic distance (distance between cation and anion, or half the unit cell length a ) in some rock-salt-structure crystals are: 2.3 Å (2.3 × 10 −10 m) for ...
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