By Riseborough P.S.
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Additional resources for Condensed matter physics I
Each atom is covalently bonded to four other atoms. The four neighboring atoms form a tetrahedron centered on each atom. The tetrahedra centered on the two inequivalent lattice sites have different orientations. The diamond lattice is most stable for compounds in which the bonds are highly directional. Directional covalent bonding is often found in the elements of column IV of the periodic table. In particular, Carbon, Silicon and Germanium can crystallize in the diamond structure. The great strength of diamond is a consequence of the three-dimensional network of strong covalent bonds.
Here the point groups are enumerated according to the Bravais Lattice types and by the Schoenflies designation followed by the appropriate (International) symbol. The cubic system with a basis can have the point symmetry group of either Oh (m3m), O (43), Td (43m), Th (m3) or T (23). The tetragonal system can have point group symmetry of D4h (4/mmm), D4 (42), C4v (4mmm), C4h (4/m) or C4 (4). The orthorhombic system can have point group symmetry of either D2h (mmm), D2 (222) or C2v (2mm). The monoclinic system can exist with point group symmetry of either C2h (2/m), C2 (2) and Cs (m), the group which only consists of the identity and the inversion operation.
A glide operation is composed of a translation by a vector, not in the Bravais lattice, which is followed by a reflection in a plane containing the translation vector. Glide planes are denoted by a, b, c (according to whether the translation is along the a, b and c axis), or n and d (the diagonal or diamond glide which are special cases involving translations along more than one axis). The hexagonal close packed lattice structure has both of these types of nonsymmorphic symmetry operations. The hexagonal close packed structure can be described by a three-dimensional unit cell which contains a centered hexagonal base, and which has an identical centered hexagonal top located at vertical distance c directly above the base.