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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 .
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.
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:
K = 1.20200 × 10 −4 J·m·mol −1: d = 3.45 × 10 −11 m ν is the number of ions in the empirical formula, z + and z − are the numbers of elementary charge on the cation and anion, respectively, and r + and r − are the radii of the cation and anion, respectively, in meters.
The allowed size of the cation for a given structure is determined by the critical radius ratio. [2] If the cation is too small, then it will attract the anions into each other and they will collide hence the compound will be unstable due to anion-anion repulsion; this occurs when the radius ratio drops below the critical radius ratio for that ...
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 ]
Many of these methods give the sum of anion and cation contributions but some can work out values for independent ions. For monoatomic ions, decreasing ionic radius shows decreasing conductivity suggesting that the effective radius of the hydrated ion increases as ionic radius decreases (larger ions are less mobile so their ability to move ...
If this convention is used, then the values are in the same range as monovalent ions, e.g. 59.5 S cm 2 mol −1 for 1 / 2 Ca 2+ and 80.0 S cm 2 mol −1 for 1 / 2 SO 2− 4. [4] From the ionic molar conductivities of cations and anions, effective ionic radii can be calculated using the concept of Stokes radius. The values ...
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