Pauling's rules of linkage

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The Pauling linking rules are five rules in 1929 by Linus Pauling published. They are used to determine the crystal structure of ionically built crystals and thus represent one of the fundamentals of crystal chemistry .

1. A coordination polyhedron of anions is formed around each cation . The cation-anion distance is determined by the sum of the ionic radii , the coordination number (KZ for short) by the radius ratio (r K / r A ).

Examples of radius ratios and associated coordination polyhedra (the closest packing of spheres have a coordination number of 12) are:

Radius ratio concentration camp polyhedron Example ( anion complex or crystal structure)
<0.155 2 linear coordination (NO 2 ) 2−
0.155-0.225 3 triangle (CO 3 ) 2−
0.225-0.414 4th Tetrahedron Zinc sulfide (ZnS)
0.414-0.732 6th octahedron Sodium chloride (NaCl)
0.732-1,000 8th Hexahedron Cesium Chloride (CsCl)
1,000 12 cubic: cuboctahedron ; hexagonal: disheptahedron Copper (Cu) (cubic)

2. An ionic structure is stable if the sum of the strengths of the electrostatic bonds of each anion to all of the nearest cations is equal in magnitude to the charge of this anion. This means that a stable ionic structure maintains local electrical neutrality. In mathematical terms:

where is the charge of the anion and the sum is formed over the adjacent (closest) cations.

For cations with an O 2 anion, the bond strengths are, for example:

cation Radius ratio concentration camp Electrostatic bond strength
Li + 0.34 4th 0.25
Mg 2+ 0.47 6th 0.33
Sc 3+ 0.60 6th 0.5

3. Common edges and in particular areas of two coordination polyhedra reduce the stability of the structure. This effect is greater, the greater the charge on the cations and the smaller the coordination number. This effect is due to the fact that the cations come closer to each other when their coordination polyhedra are linked than when they are linked by edges or tips. The repulsive interaction becomes stronger. It is particularly pronounced when the radius ratio is close to the lower limit for the polyhedron stability.

4. In a crystal with different cations, those with high valence (high charge) and low coordination number tend not to share polyhedral elements. This is why the Si 4+ and Al 3+ tetrahedra in aluminosilicates are usually connected to one another via corners and rarely via edges.

5. The number of different constituents (or components) of a crystal tends to be as small as possible. This means, for example, that similar environments are created for chemically similar atoms / ions.

Individual evidence

  1. ↑ Linus Pauling: THE PRINCIPLES DETERMINING THE STRUCTURE OF COMPLEX IONIC CRYSTALS. In: Journal of the American Chemical Society. 51, 1929, pp. 1010-1026, doi: 10.1021 / ja01379a006 .
  2. ^ Hermann Salmang, Horst Scholze, Rainer Telle: Ceramics . Springer, 2006, ISBN 3-540-63273-5 , pp. 32 ( limited preview in Google Book search).

literature

  • Linus Pauling: The nature of chemical bonds. Reprint of the 3rd edition. Verlag Chemie, Weinheim. 1973, ISBN 3-527-25217-7 . P. 507 ff.
  • Ulrich Müller: "Inorganic Structural Chemistry." 4th revised edition. BG Teubner Verlag, Wiesbaden. 2004, ISBN 3-519-33512-3 , pp. 59 ff.