Diamond structure

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The diamond structure (also diamond lattice , A4 type or diamond type ) is a crystal structure , i.e. the arrangement pattern of the atoms of a crystalline material. This type of structure was discovered in diamonds , a modification of carbon , but other materials with atoms from main group 4 ( tetravalent elements ) can also crystallize in this structure, for example silicon , germanium and silicon-germanium alloys as well as α- tin . Analogous to crystalline diamonds, low-molecular compounds of carbon can also have the diamond structure, so-called diamondoids . Its simplest representative is adamantane .

construction

Four sp 3 hybrid orbitals are tetrahedrally aligned at the same angle to one another.

The diamond structure consists of a face- centered cubic lattice and the base {(0,0,0), (1 / 4.1 / 4.1 / 4)}. The diamond structure can also be clearly described as a combination of two face-centered cubic lattices, which are shifted from one another by 1/4 of the spatial diagonal .

Each carbon atom is covalently bonded to four neighboring atoms. The diamond structure thus 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) in the zinc blende structure of two different ions are occupied. In both structures, each atom is connected to 4 atoms of the same element (in the case of diamond, carbon atoms). The reason for this is the hybridization of the atomic orbitals of the outermost shell of the ground state (carbon: 1s 2 2s 2 2p 2 ) to four sp3 hybrid orbitals (1s 2 2 [sp 3 ] 4 ). Due to the electromagnetic repulsion, these four orbitals are oriented symmetrically in space with the greatest possible distance or angle (109 ° 28 ') to each other, they point to the corners of an imaginary tetrahedron .

Simplifying two-dimensional images of grids with tetravalent elements show a common two-dimensional grid pattern. In three-dimensional space, however, the four valence electrons occupy a position that corresponds to the four corners of a tetrahedron, with the atomic nucleus in the center of the tetrahedron. In 2D representations of the 3D structure of diamonds, the atom is drawn from which the four corners of the tetrahedron extend in four bonds (valences).

When looking at this tetrahedron of the diamond structure, there are three valences at the three corners of an equilateral triangle and touch three neighboring atoms that lie in a common plane. The fourth valence lies in the middle of the triangle and touches a fourth neighboring atom in another plane - closer to the viewer or further away from the viewer. In the diamond structure, the tetrahedra are alternately rotated so that the fourth valence points towards and away from the observer.

symmetry

Stereographic projection of the diamond structure in the [111] direction

The diamond structure has the space group Fd 3 m (space group no. 227) . So it is a cubic crystal structure. Template: room group / 227

Fd 3 m (No. 227) is the abbreviated form of F 4 1 / d 3 2 / m . F means that the Bravais lattice is face-centered, 4 1 / d means a 4 1 screw axis parallel to the crystallographic a-axis (rotation by 90 ° and displacement ( translation ) by 1/4 in the direction of the a-axis), the 4 1 screw axis is still perpendicular to a "diamond sliding mirror plane" ( d ). There are threefold rotational inversion axes 3 along the spatial diagonals of the unit cell . There are twofold axes of rotation (2) parallel to the diagonals of the surfaces of the unit cell and mirror planes ( m ) perpendicular to them . (See also: Hermann Mauguin symbol ) Template: room group / 227

properties

As mentioned, the typical tetravalent semiconductors such as silicon and germanium crystallize in the diamond structure. Due to the strong covalent bonds, there are no free electrons and the materials have saturated valences at T  = 0 K (temperature at absolute zero ), i.e. H. fully occupied valence bands (VB). The conduction band (LB), however, is completely empty. Pure semiconductors without crystal defects are therefore insulators at T  = 0 K , because no charge carriers ( electrons or defective electrons ) are available to transport electricity.

The band structure of materials with a diamond structure usually has an energy gap (indirect band gap ). This takes on different values ​​depending on the element (at 300 K: E g, diamond  = 5.33  eV , E g, silicon  = 1.14 eV, E g, germanium = 0.67 eV, E g, tin = 0, 08 eV). With the low values ​​for the energy gap for silicon, germanium and tin, the thermal energy at room temperature is sufficient to lift electrons from the valence band into the conduction band. The electrons in the LB and the remaining defect electrons in the VB can now conduct the electric current under the influence of an externally applied electric field. This transition of electrons from the valence band to the conduction band can also be caused by photons ( photoelectric effect ). In addition, the energy gap can be reduced through targeted contamination ( doping ) and the resulting traps (localized) and thus the conductivity can be increased ( impurity conduction ).

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

The particular hardness of diamond cannot be explained with the structural model alone; it is a consequence of the particularly firm and directed covalent bonds that the tetrahedral sp 3 orbitals of carbon form.

literature

  • Rudolf Gross, Achim Marx: Solid State Physics. Oldenbourg Wissenschaftsverlag, 2012, ISBN 978-3486712940 .

Web links

Commons : Diamond cubic  - album with pictures, videos and audio files

Individual evidence

  1. ^ Rudolf Gross, Achim Marx: Solid State Physics . Oldenbourg Verlag, 2012, ISBN 3-486-71294-2 , p. 31 ( limited preview in Google Book search).
  2. ^ Kurt Peter C. Vollhardt, Neil E. Schore: Organic chemistry . John Wiley & Sons, 2011, ISBN 3-527-32754-1 , pp. 168 ( limited preview in Google Book search).
  3. Charles Kittel : Introduction to Solid State Physics . Oldenbourg Verlag, 2013, ISBN 3-486-59755-8 , p. 20 ( limited preview in Google Book search).
  4. a b Will Kleber , Hans-Joachim Bautsch , Joachim Bohm : Introduction to Crystallography - Will Kleber, Hans-Joachim Bautsch, Joachim Bohm . Oldenbourg Verlag, 2002, ISBN 3-486-59885-6 , p. 157 ( limited preview in Google Book search).
  5. Koji Kobashi: Diamond films: chemical vapor deposition for oriented and heteroepitaxial growth . Elsevier, 2005, ISBN 978-0-08-044723-0 , 2.1 Structure of diamond, p. 9 .
  6. Text on Cubic Diamond . University of Konstanz. Retrieved August 30, 2011.
  7. Werner Massa: Crystal structure determination . Springer DE, 2009, ISBN 3-8348-9593-8 , p. 67 ( limited preview in Google Book search).
  8. Walter J. Moore: Fundamentals of physical chemistry . Walter de Gruyter, 1990, ISBN 3-11-009941-1 , p. 744 ( limited preview in Google Book search).
  9. Horst Briehl: Chemistry of materials . Springer, 2007, ISBN 3-8351-0223-0 , pp. 29 ( limited preview in Google Book search).