Octahedral gap

Octahedral gap in a cubic closest packing of spheres

The octahedral gap in a crystal structure is a cavity formed by at least six neighboring atoms or ions . This remains free even if the atoms are placed as close as possible in the closest packing of spheres . The name comes from the fact that the atoms form an octahedron . In addition to the larger octahedron gaps, the closest packing of spheres also have the smaller tetrahedron gaps , which are formed by only four atoms.

An octahedral gap in the face-centered cubic crystal is placed exactly in the center of the unit cell . In addition, there are 12 more octahedral gaps that lie exactly in the middle of the edges of the unit cell. These "edge octahedral gaps" are shared with four neighboring unit cells. The total number of octahedral holes per unit cell is therefore 1 + 12 · 1/4 = 4. In principle, densest spherical packings have as many octahedral holes as atoms in the unit cell.

Smaller foreign atoms can be embedded in these octahedral gaps. These can be installed irregularly as defects or regularly as connection partners. An example of regular installation is the sodium chloride structure . In sodium chloride , the chloride anions are about twice as large as the sodium cations. The anions form a tightly packed face-centered cubic lattice, the cations fill in the octahedral gaps.

The size of the octahedral gap can be given by the radius r of the largest sphere that fits into the gap. With the radius of the sphere of the octahedron

{\ displaystyle r_ {u} = {\ frac {\ sqrt {2}} {2}} a}

and the radius R of the large spheres in the corners of the octahedron and the side length a = 2 R of the octahedron are obtained for the octahedral gaps of the face-centered cubic lattice

{\ displaystyle r = r_ {u} -R = \ left ({\ sqrt {2}} - 1 \ right) R \ approx 0 {,} 414R}

.

and for the body-centered cubic lattice with : ${\ displaystyle a = {\ frac {4 {\ sqrt {3}} R} {3}}}$

{\ displaystyle r = {\ frac {a} {2}} - R = \ left ({\ frac {2} {3}} {\ sqrt {3}} - 1 \ right) R \ approx 0 {,} 155R}

Individual evidence

^ Charles E. Mortimer, Ulrich Müller: Chemistry - The basic knowledge of chemistry. 12th edition, Georg Thieme Verlag, 2015, ISBN 978-3-13-484312-5 , p. 188.

literature

Ulrich Müller: Inorganic Structural Chemistry. 5th edition, Teubner, Stuttgart 2006, ISBN 3-83-510107-2 , p. 278 ff.

Web links

Java applet from ChemgaPedia

[1] Charles E. Mortimer, Ulrich Müller: Chemistry - The basic knowledge of chemistry. 12th edition, Georg Thieme Verlag, 2015, ISBN 978-3-13-484312-5 , p. 188.