Crystal family

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Famille cristalline (Fr); Famiglia cristallina (It); 晶ファミリー (Ja).

Contents

Definition

A crystal family is the smallest set of space groups containing, for any of its members, all space groups of the Bravais flock and all space groups of the geometric crystal class to which this member belongs.

Features

Two crystals belong to the same crystal family if they have the same type of conventional cell, differing only for the presence or absence of centring nodes.

For example, an orthorhombic crystal with primitive lattice and an orthorhombic crystal with face-centred lattice belong to the same crystal family (orthorhombic). Their conventional cells both have orthorhombic metric.

In the two-dimensional space, all the lattices belonging to the same crystal family have the same symmetry. In the three-dimensional space, the same holds for five of the six crystal families. In the hexagonal crystal family however, the two lattices have different symmetry: -32/m (rhombohedral) and 6/m2/m2/m (hexagonal). Consequently, the hexagonal crystal family splits into two lattice systems: rhombohedral and hexagonal.

Rhombohedral crystals belong to the trigonal crystal system, but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system.

Crystal families in two and three dimensions

In the two-dimensional space there exist four crystal families:

  • monoclinic (m )
  • orthorhombic (o )
  • tetragonal (t )
  • hexagonal (h )

In the three-dimensional space there exist six crystal families:

  • triclinic (a, for 'anorthic')
  • monoclinic (m )
  • orthorhombic (o )
  • tetragonal (t )
  • hexagonal (h )
  • cubic (c )

See also