Difference between revisions of "Crystal family"
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| − | <font color="blue">Famille cristalline </font>(''Fr'') | + | <font color="blue">Famille cristalline</font> (''Fr''). <font color="black">Famiglia cristallina</font> (''It''). <font color="purple">結晶族</font> (''Ja''). |
== Definition == | == Definition == | ||
| − | A '''crystal family''' is the smallest set of space groups containing, for any of its members, all space groups of the [[Bravais | + | A '''crystal family''' is the smallest set of space groups containing, for any of its members, all space groups of the [[Bravais class]] and all space groups of the [[geometric crystal class]] to which this member belongs. |
== Features == | == Features == | ||
| − | Two crystals belong to the same crystal family if they have the same type of [[conventional cell]], differing only | + | Two crystals belong to the same crystal family if they have the same type of [[conventional cell]], differing only in 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. | 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/''m''2/''m''2/''m'' (hexagonal). Consequently, the hexagonal crystal family splits into two [[lattice system]]s: | + | 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/''m''2/''m''2/''m'' (hexagonal). Consequently, the hexagonal crystal family splits into two [[lattice system]]s: 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 == | == Crystal families in two and three dimensions == | ||
| − | In | + | In two-dimensional space there exist four crystal families: |
| − | * monoclinic (''m'' ) | + | * monoclinic (''m'') |
| − | * orthorhombic (''o'' ) | + | * orthorhombic (''o'') |
| − | * tetragonal (''t'' ) | + | * tetragonal (''t'') |
| − | * hexagonal (''h'' ) | + | * hexagonal (''h'') |
| − | In | + | In three-dimensional space there exist six crystal families: |
* triclinic (''a'', for 'anorthic') | * triclinic (''a'', for 'anorthic') | ||
| − | * monoclinic (''m'' ) | + | * monoclinic (''m'') |
| − | * orthorhombic (''o'' ) | + | * orthorhombic (''o'') |
| − | * tetragonal (''t'' ) | + | * tetragonal (''t'') |
| − | * hexagonal (''h'' ) | + | * hexagonal (''h'') |
| − | * cubic (''c'' ) | + | * cubic (''c'') |
== See also == | == See also == | ||
*[[Crystal system]] | *[[Crystal system]] | ||
*[[Lattice system]] | *[[Lattice system]] | ||
| − | * | + | *Chapter 1.3.4.4.4 of ''International Tables for Crystallography, Volume A'', 6th edition |
[[category: Fundamental crystallography]] | [[category: Fundamental crystallography]] | ||
Latest revision as of 17:24, 30 May 2019
Famille cristalline (Fr). Famiglia cristallina (It). 結晶族 (Ja).
Definition
A crystal family is the smallest set of space groups containing, for any of its members, all space groups of the Bravais class 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 in 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 two-dimensional space there exist four crystal families:
- monoclinic (m)
- orthorhombic (o)
- tetragonal (t)
- hexagonal (h)
In three-dimensional space there exist six crystal families:
- triclinic (a, for 'anorthic')
- monoclinic (m)
- orthorhombic (o)
- tetragonal (t)
- hexagonal (h)
- cubic (c)
See also
- Crystal system
- Lattice system
- Chapter 1.3.4.4.4 of International Tables for Crystallography, Volume A, 6th edition