Tetrahedral gap

Tetrahedral gap

The tetrahedron gap is the cavity in a tetrahedron that remains free when spheres that touch each other are placed in the corners of the tetrahedron.

Many crystals have structures in which the atoms locally form a tetrahedron. These structure types include, among other things, the closest packing of spheres, i.e. above all the face-centered cubic lattice and the hexagonal closest packing of spheres . Closest packing of spheres always have twice as many tetrahedral gaps as spheres. Smaller foreign atoms can be incorporated into these tetrahedral gaps.

These can be installed irregularly as defects or regularly as connection partners. The fluorine atoms in the tetrahedral gaps of the face-centered cubic calcium lattice in fluorite are an example of regular installation .

In the model of the packing of spheres , the atoms or ions are usually thought of as (approximately) rigid spheres - according to the definition of the ion radius . The size of the tetrahedral gap can then be given by the radius r of the sphere that fits exactly into the gap. With the radius of the sphere r _{u of} the tetrahedron

${\displaystyle r_{u}={\frac {\sqrt {6}}{4}}a}$

and the radius R of the large spheres in the corners of the tetrahedron and the side length a = 2 R of the tetrahedron are obtained

${\displaystyle r=r_{u}-R={\frac {1}{2}}\left({\sqrt {6}}-2\right)R\approx 0{,}22474487\cdot R}$.

See also

Commons : Tetrahedron Gap  - album with pictures, videos and audio files

• Octahedral gap

Individual evidence

1. ^ Charles E. Mortimer, Ulrich Müller: Chemistry - The basic knowledge of chemistry. Georg Thieme Verlag, 2003, ISBN 3-13-484308-0 , p. 183.