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In condensed matter physics and inorganic chemistry, the cation-anion radius ratio can be used to predict the crystal structure of an ionic compound based on the relative size of its atoms. It is defined as the ratio of the ionic radius of the positively charged cation to the ionic radius of the negatively charged anion in a cation-anion ...
For typical ionic solids, the cations are smaller than the anions, and each cation is surrounded by coordinated anions which form a polyhedron.The sum of the ionic radii determines the cation-anion distance, while the cation-anion radius ratio + / (or /) determines the coordination number (C.N.) of the cation, as well as the shape of the coordinated polyhedron of anions.
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 .
In inorganic chemistry, Fajans' rules, formulated by Kazimierz Fajans in 1923, [1] [2] [3] are used to predict whether a chemical bond will be covalent or ionic, and depend on the charge on the cation and the relative sizes of the cation and anion. They can be summarized in the following table:
Finally, Kapustinskii noted that the Madelung constant, M, was approximately 0.88 times the number of ions in the empirical formula. [2] The derivation of the later form of the Kapustinskii equation followed similar logic, starting from the quantum chemical treatment in which the final term is 1 − d / r 0 where d is as defined
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 ]
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