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.

A rhombohedral crystal and a hexagonal crystal both belong to the hexagonal crystal family. In fact, the conventional cell of a rhombohedral crystal is hexagonal.

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