3.4 Important Crystal Structures
45
Fig. 3.15 a Rocksalt
(NaCl) structure, b CsCl
structure
(a)
(b)
Fig. 3.16 a Diamond
structure and b zincblende
structure (red spheres: A
atoms, green spheres: B
atoms). The tetragonal
bonds are indicated
(a)
(b)
3.4.1 Rocksalt Structure
The rocksalt (rs, NaCl, space group 225, Fm ¯
3m) structure (Fig. 3.15a) consists of a fcc lattice with
the period a and a diatomic base in which the Cl atom is positioned at (0,0,0) and the Na atom
at (1/2,1/2,1/2)a with a distance
√
3 a/2. Materials that crystallize (under normal conditions) in the
rocksalt lattice are, e.g., KCl, KBr, PbS (galena), PbSe, PbTe, AgBr, MgO, CdO, MnO. AlN, GaN and
InN undergo, under high pressure, a phase transition from the wurtzite into the rocksalt structure.
3.4.2 CsCl Structure
The CsCl structure (space group 221, Pm ¯
3m) (Fig. 3.15b) consists of a simple cubic lattice. Similar
as for the rocksalt structure, the base consists of different atoms at (0,0,0) and (1/2,1/2,1/2)a. Typical
crystals with CsCl-structure are TlBr, TlI, CuZn (β-brass), AlNi.
3.4.3 Diamond Structure
The diamond structure (C, space group 227, Fd ¯
3m) (Fig. 3.16a) has the fcc lattice. The base consists
of two identical atoms at (0,0,0) and (1/4,1/4,1/4)a. Each atom has a tetrahedral configuration. The
packing density is only about 0.34. The ABC-type stacking along the [111]-direction is visualized in
Fig. 3.17a. The materials that crystallize in the diamond lattice are C, Ge, Si and α-Sn. Silicon as the
most important semiconductor is particularly well researched [205].
The diamond structure (point group O h ) has an inversion center, located between the two atoms of
the base, i.e. at (1/8,1/8,1/8)a. The radii of the wavefunctions for various group-IV elements increases
with the order number (Table 3.2), and accordingly the lattice constant increases.
In Fig. 3.18a the unit cell with tetragonal symmetry of three places along the 111 direction is
shown. In Fig. 3.18b the arrangement of atoms along 111 is depicted. The symmetry along this line is
at least C 3v . At the atoms sites it is O h . The bond center (BC) and the hexagonal (H) position are a center
of inversion and have D 3d symmetry. The unoccupied ‘T’ positions have T d symmetry. High-pressure
phases of silicon are already found in indentation experiments [206].
45
Fig. 3.15 a Rocksalt
(NaCl) structure, b CsCl
structure
(a)
(b)
Fig. 3.16 a Diamond
structure and b zincblende
structure (red spheres: A
atoms, green spheres: B
atoms). The tetragonal
bonds are indicated
(a)
(b)
3.4.1 Rocksalt Structure
The rocksalt (rs, NaCl, space group 225, Fm ¯
3m) structure (Fig. 3.15a) consists of a fcc lattice with
the period a and a diatomic base in which the Cl atom is positioned at (0,0,0) and the Na atom
at (1/2,1/2,1/2)a with a distance
√
3 a/2. Materials that crystallize (under normal conditions) in the
rocksalt lattice are, e.g., KCl, KBr, PbS (galena), PbSe, PbTe, AgBr, MgO, CdO, MnO. AlN, GaN and
InN undergo, under high pressure, a phase transition from the wurtzite into the rocksalt structure.
3.4.2 CsCl Structure
The CsCl structure (space group 221, Pm ¯
3m) (Fig. 3.15b) consists of a simple cubic lattice. Similar
as for the rocksalt structure, the base consists of different atoms at (0,0,0) and (1/2,1/2,1/2)a. Typical
crystals with CsCl-structure are TlBr, TlI, CuZn (β-brass), AlNi.
3.4.3 Diamond Structure
The diamond structure (C, space group 227, Fd ¯
3m) (Fig. 3.16a) has the fcc lattice. The base consists
of two identical atoms at (0,0,0) and (1/4,1/4,1/4)a. Each atom has a tetrahedral configuration. The
packing density is only about 0.34. The ABC-type stacking along the [111]-direction is visualized in
Fig. 3.17a. The materials that crystallize in the diamond lattice are C, Ge, Si and α-Sn. Silicon as the
most important semiconductor is particularly well researched [205].
The diamond structure (point group O h ) has an inversion center, located between the two atoms of
the base, i.e. at (1/8,1/8,1/8)a. The radii of the wavefunctions for various group-IV elements increases
with the order number (Table 3.2), and accordingly the lattice constant increases.
In Fig. 3.18a the unit cell with tetragonal symmetry of three places along the 111 direction is
shown. In Fig. 3.18b the arrangement of atoms along 111 is depicted. The symmetry along this line is
at least C 3v . At the atoms sites it is O h . The bond center (BC) and the hexagonal (H) position are a center
of inversion and have D 3d symmetry. The unoccupied ‘T’ positions have T d symmetry. High-pressure
phases of silicon are already found in indentation experiments [206].