Diamond cubic

The diamond structure (including diamond or diamond lattice type) is a crystal structure, that is, the arrangement pattern of atoms in a crystalline material. This type of structure in the diamond, a form of carbon, but other materials with atoms from the main group 4 was discovered ( tetravalent elements ) can crystallize in this structure, such as silicon, germanium and silicon -germanium alloys and α - tin. Similar to the crystalline diamond can also low molecular weight compounds of carbon have the diamond structure, so-called Diamondoids. Your simplest representative is the adamantane.

Construction

The diamond structure is a face-centered cubic lattice and the base { (0,0,0 ), (1 /4, 1 /4, 1 /4) }. Clearly, one can describe the diamond structure as a combination of two concentric asked face-centered cubic lattice, which are shifted by 1 /4 of the space diagonal to each other.

Each carbon atom is covalently bonded equivalent with four neighboring atoms. The diamond structure therefore corresponds to the zinc-blende structure ( ZnS), with the difference that the two crystallographic layers ( 0,0,0 ) and (1 /4, 1 /4, 1 /4) different in the zinc blende structure of two ion are occupied. In both structures, each atom with atoms of the same element 4 is connected ( in diamond carbon atoms). The reason for this is the hybridization of the atomic orbitals of the outermost shell of the ground state ( carbon: 1s22s22p2 ) to four sp3 hybrid orbitals ( 1s2 2 [ sp3 ] 4). These four orbitals are symmetrical to each other -oriented due to the electromagnetic repulsion with the greatest possible distance or angle ( 109.5 ° ) in the space, they show in the corners of an imaginary tetrahedron.

Simplistic two-dimensional images of gratings with tetravalent elements show an ordinary two-dimensional grid pattern. However, in three-dimensional space, the four valence electrons to take a position corresponding to the four corners of a tetrahedron, with the nucleus is located in the center of the tetrahedron. In 2D representations of the 3D structure of diamonds the atom is drawn, from which stretch out the four corners of the tetrahedron in four bonds ( valences ).

In view of this tetrahedron, the diamond structure are three valences of the three corners of an equilateral triangle and three adjacent touch atoms lie in a common plane. The fourth valency of the triangle is located in the center and contacts a fourth adjacent atom in a different level - closer to the viewer or further away from the viewer. In the diamond structure of the tetrahedra are rotated alternately in such a way that the fourth valency points towards the viewer, or away from him.

Crystallographic space group

The diamond structure has the space group. Thus, it is a cubic crystal structure.

Is the condensed notation of. F means that the Bravais lattice is face-centered, means 41 screw axis parallel to the crystallographic a - axis ( 90 ° rotation and displacement (translation ) by 1/ 4 in the direction of the a- axis), the 41 - coil axis is further vertically on a " Diamantgleitspiegelebene " (d). Along the space diagonal of the unit cell are threefold rotational inversion axes. Parallel to the diagonals of the faces of the unit cell there are two-fold rotation axes ( 2) and perpendicular to mirror planes (m). (See also: Hermann- Mauguin symbol )

Properties

As mentioned crystallize typical tetravalent semiconductors such as silicon and germanium in the diamond structure. Due to the strong covalent bonds, there are no free electrons and the materials have at T = 0 K (temperature at absolute zero ) unsatisfied valence, that is fully occupied valence bands (VB), on. The conduction band (LB ) on the other hand is completely empty. Pure semiconductors are therefore free of crystal at T = 0 K insulators, because there are no charge carriers ( electrons or holes ) for the current transport.

The band structure of materials having a diamond structure usually has an energy gap ( band gap). This takes different values ​​depending on the element at ( Eg = 5.4 eV diamond, Eg, silicon = 1.1 eV). At the low values ​​of the energy gap in silicon, and germanium (0.67 eV) is already sufficient, the thermal energy at room temperature in order to raise the electrons from the valence band to the conduction band. The electrons in the LB and the remaining electrons in the defect VB can now conduct the electrical current, under the influence of an externally applied electric field. This transition of electrons from the valence band to the conduction band can be caused by photons ( photoelectric effect). In addition, the energy gap by selectively contaminating (doping ) and its resulting adhesion sites ( localized ) can be reduced and thus the conductivity can be increased ( extrinsic ).

Since only four of the eight tetrahedral gaps are occupied by carbon atoms in the diamond, the grid is relatively thick expanded. The packing density of the diamond lattice - not only in diamond - is thus comparatively small, only about 34 percent of the available lattice volume are occupied.

The particular hardness of diamond can be with the lattice model does not explain, it is a consequence of the particularly solid and directional covalent bonds that enter into the tetrahedral sp3 orbitals of carbon.