Ionic radius

Size of the atoms and ions of some chemical elements in picometers (gray: atoms, red: cations, blue: anions).

The ion radius describes the effective size of a monatomic ion in an ion lattice . For the sake of simplicity, it is assumed that these are rigid spheres, the radii of which are independent of the ionic compound (provided the coordination number matches). In order to determine the ion radii, one first determines the distances between the ions occurring in the crystal lattice. The sum of radii r _A + r _K for various ion combinations is obtained from these cation-anion distances . So that the radii of the individual ions can be determined, the radius of at least one of the ions involved must be known independently.

Pauling theoretically determined the value of 140 pm for an O ²⁻ ion; this value and the other ionic radii determined with it apply to the coordination number 6.

Ionic radii (selection)
see also list of ionic radii
The values given apply to the coordination number 6
ion	Ionic radius in pm
H ^-	154
F ^-	133
Cl ^-	181
O ²⁻	140
S ²⁻	184
Li ⁺	76
Na ⁺	102
K ⁺	138
NH ₄⁺	143
Cu ⁺	77
Ag ⁺	115
Au ⁺	137

Dependence on the coordination number

The ion radii are always directly related to the coordination number , because if the number of neighboring ions increases, the repulsive forces between the electron shells of the ions also increase, the consequence of which is that the equilibrium distance increases.
From experimentally determined ion radii it follows that the relative changes of the individual ions are individual and one can only give an average approximation. The following dependency results:

Coordination number	8th	6th	4th
Ionic radius	1.1	1.0	0.8

The table shows that the ion radii of one and the same ion behave as 1.1: 1.0: 0.8 for the coordination numbers 8, 6, 4.
From these values it can be concluded that the ion radii are different from the equilibrium distance in a crystal and the image of a rigid sphere does not apply to an isolated ion. In different compounds, an ion only behaves as a rigid sphere with an approximately constant radius if the number of its closest neighbors, the so-called coordination number, does not change.

Relationship with the atomic radius

Ionic radii and atomic radii are related:

in the case of cations , i.e. positively charged ions, the ionic radius is smaller than the atomic radius. The larger the positive charge, the smaller the ionic radius becomes.
in the case of anions , i.e. negatively charged ions, the ion radius is larger than the atomic radius. The larger the negative charge, the larger the ionic radius becomes.

What does the ionic radius depend on?

a) Within a group (i.e. from top to bottom in the periodic table ) the ionic radii increase, since a new atomic orbital is also present in each period and the distance between the valence electrons and the atomic nucleus increases. Within one period (i.e. from left to right in the periodic table), the ionic radius decreases as the atomic number increases, so that the attraction of the atomic nucleus to the electrons increases and the ionic radius decreases.

b) The number of valence electrons. The following rule applies: cations are always smaller than the anions of the same period. Some cations (K ⁺ , Rb ⁺ , Cs ⁺ , NH ₄⁺ , Ba ²⁺ ) are larger than the smallest anion (F ^- ). Explanation: The atomic number (= number of protons) increases from element to element within a period. This means that the valence electrons are getting stronger and stronger, attracted by more and more protons. It follows from this: The radius decreases slightly.

For ions of transition metals , the radius also depends on the spin state (see ligand field theory ).

The ratio of the ionic radii of cations / anions determines how many ions they are surrounded by ( coordination number ). a. also responsible for the crystal structure or the crystal structure type.

literature

Erwin Riedel : Inorganic Chemistry. de Gruyter, Berlin 2004, ISBN 3-11-018168-1 .
Erwin Riedel, Christoph Janiak: Inorganic Chemistry. 7th edition. de Gruyter, Berlin 2007, ISBN 978-3-11-018903-2 .

Individual evidence

↑ RD Shannon: Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides . In: Acta Cryst . A32, 1976, p. 751-767 , doi : 10.1107 / S0567739476001551 (English).
↑ Erwin Riedel, Christoph Janiak: Inorganic Chemistry. 7th edition. de Gruyter, Berlin 2007, ISBN 978-3-11-018903-2 , p. 75.
↑ Erwin Riedel, Christoph Janiak: Inorganic Chemistry. 7th edition. de Gruyter, Berlin 2007, ISBN 978-3-11-018903-2 , p. 74.

[1] RD Shannon: Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides . In: Acta Cryst . A32, 1976, p. 751-767 , doi : 10.1107 / S0567739476001551 (English).

[Ionenradien_Tabelle-2] Erwin Riedel, Christoph Janiak: Inorganic Chemistry. 7th edition. de Gruyter, Berlin 2007, ISBN 978-3-11-018903-2 , p. 75.

[Ionenradien-3] Erwin Riedel, Christoph Janiak: Inorganic Chemistry. 7th edition. de Gruyter, Berlin 2007, ISBN 978-3-11-018903-2 , p. 74.