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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.
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:
The strength of the M-O bond tends to increase with the charge and decrease as the size of the metal ion increases. In fact there is a very good linear correlation between hydration enthalpy and the ratio of charge squared to ionic radius, z 2 /r. [4] For ions in solution Shannon's "effective ionic radius" is the measure most often used. [5]
Under some definitions, the value of the radius may depend on the atom's state and context. [1] Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease rightward along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group ...
The first attempt to measure the mass-to-charge ratio of cathode ray particles, assuming them to be ions, was made in 1884-1890 by German-born British physicist Arthur Schuster. He put an upper limit of 10^10 coul/kg, [ 5 ] but even that resulted in much greater value than expected, so little credence was given to his calculations at the time.
Toggle the table of contents. ... is a dimensionless number that is calculated from the ratio of the ionic radii: [1] ... r A is the radius of the A cation.