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The radius ratio rules are a first approximation which have some success in predicting coordination numbers, but many exceptions do exist. [3] In a set of over 5000 oxides, only 66% of coordination environments agree with Pauling's first rule. Oxides formed with alkali or alkali-earth metal cations that contain multiple cation coordinations are ...
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 .
See also: Electronegativities of the elements (data page) There are no reliable sources for Pm, Eu and Yb other than the range of 1.1–1.2; see Pauling, Linus (1960).
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 .
The bond valence method is a development of Pauling's rules. In 1930, Lawrence Bragg [11] showed that Pauling's electrostatic valence rule could be represented by electrostatic lines of force emanating from cations in proportion to the cation charge and ending on anions. The lines of force are divided equally between the bonds to the corners of ...
In essence the Hume-Rothery rules (and Pauling's rules) are based on geometrical restraints. Likewise are the advancements being done to the Hume-Rothery rules. Where they are being considered as critical contact criterion describable with Voronoi diagrams. [8] This could ease the theoretical phase diagram generation of multicomponent systems.
See also: Electronegativities of the elements (data page) There are no reliable sources for Pm, Eu and Yb other than the range of 1.1–1.2; see Pauling, Linus (1960).
[34] [35] Depending on the stoichiometry of the salt, and the coordination (principally determined by the radius ratio) of cations and anions, a variety of structures are commonly observed, [36] and theoretically rationalized by Pauling's rules.