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. Anions are larger than cations. Large sized anions occupy lattice sites, while small sized cations are found in voids. In a given structure, the ratio of cation radius to anion radius is called the radius ratio. This is simply given by .
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. 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 particular structure. At the stability limit the cation is touching all the anions and the anions are just touching at their edges. For radius ratios greater than the critical ratius ratio, the structure is expected to be stable.
The rule is not obeyed for all compounds. By one estimate, the crystal structure can only be guessed about 2/3 of the time. [3] Errors in prediction are partly due to the fact that real chemical compounds are not purely ionic, they display some covalent character. [1]
The table below gives the relation between critical radius ratio, , and coordination number, , which may be obtained from a simple geometrical proof. [4]
Critical Radius Ratio | Coordination number | Type of void | Crystal structure | Examples |
---|---|---|---|---|
0.1547 | 3 | Trigonal planar | α-B2O3 structure | B2O3 |
0.2247 | 4 | Tetrahedral | Zincblende structure | ZnS, CuCl |
0.4142 | 6 | Octahedral | Rock salt structure | NaCl, MgO |
0.7320 | 8 | Cubic | CsCl structure | CsCl, NH4Br |
The radius ratio rule was first proposed by Gustav F. Hüttig in 1920. [5] [6] In 1926, Victor Goldschmidt [5] extended the use to ionic lattices. [7] [8] [9] In 1929, the rule was incorporated as the first of Pauling's rules for crystal structures. [10]
Electronegativity, symbolized as χ, is the tendency for an atom of a given chemical element to attract shared electrons when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. Electronegativity serves as a simple way to quantitatively estimate the bond energy, and the sign and magnitude of a bond's chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding. The loosely defined term electropositivity is the opposite of electronegativity: it characterizes an element's tendency to donate valence electrons.
Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding, along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be more complex, e.g. molecular ions like NH+
4 or SO2−
4. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal to obtain a full valence shell for both atoms.
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3. This anion, one of the polyhalogen ions, is composed of three iodine atoms. It is formed by combining aqueous solutions of iodide salts and iodine. Some salts of the anion have been isolated, including thallium(I) triiodide (Tl+[I3]−) and ammonium triiodide ([NH4]+[I3]−). Triiodide is observed to be a red colour in solution.
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