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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 compound.
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.
Cations and anions are measured by their ionic radius and they differ in relative size: "Cations are small, most of them less than 10 −10 m (10 −8 cm) in radius. But most anions are large, as is the most common Earth anion, oxygen. From this fact it is apparent that most of the space of a crystal is occupied by the anion and that the ...
Common ionic compound structures with close-packed anions [36] Stoichiometry Cation:anion coordination Interstitial sites Cubic close packing of anions Hexagonal close packing of anions Occupancy Critical radius ratio Name Madelung constant Name Madelung constant MX: 6:6: all octahedral: 0.4142 [34] sodium chloride: 1.747565 [38] nickeline <1. ...
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:
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 calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%.
Ionic radius: the nominal radius of the ions of an element in a specific ionization state, deduced from the spacing of atomic nuclei in crystalline salts that include that ion. In principle, the spacing between two adjacent oppositely charged ions (the length of the ionic bond between them) should equal the sum of their ionic radii. [13]