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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.
r B is the radius of the B cation. r O is the radius of the anion (usually oxygen). In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation: [ 1 ]
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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Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
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