Tetragonal crystal system

Short description: Lattice point group

An example of the tetragonal crystals, wulfenite

Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system.

In crystallography, the tetragonal crystal system is one of the 7 crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c, which is different from a).

## Contents

* 1 Bravais lattices
* 2 Crystal classes
* 3 In two dimensions
* 4 See also
* 5 References
* 6 External links

## Bravais lattices

Further information: Bravais lattice

There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal.

Bravais lattice  | Primitive
tetragonal  | Body-centered
tetragonal

|
|

Pearson symbol | tP  | tI
Unit cell |  |

The base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell.[1]

## Crystal classes

Further information: Crystallographic point group

The point groups that fall under this crystal system are listed below, followed by their representations in international notation, Schoenflies notation, orbifold notation, Coxeter notation and mineral examples.[2][3]

#  | Point group  | Type  | Example  | Space groups

|
|
|
|

Name[4] | Intl | Schoen. | Orb. | Cox.  | Primitive  | Body-centered
75–80  | Tetragonal pyramidal  | 4  | C4 | 44  | [4]+ | enantiomorphic polar | pinnoite,
piypite | P4, P41, P42, P43 | I4, I41
81–82  | Tetragonal disphenoidal  | 4 | S4 | 2×  | [2+,4+]  |  | cahnite, tugtupite | P4 | I4
83–88  | Tetragonal dipyramidal  | 4/m  | C4h | 4*  | [2,4+]  | centrosymmetric  | scheelite, wulfenite, leucite | P4/m, P42/m, P4/n, P42/n  | I4/m, I41/a
89–98  | Tetragonal trapezohedral  | 422  | D4 | 224  | [2,4]+ | enantiomorphic  | cristobalite, wardite | P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212  | I422, I4122
99–110  | Ditetragonal pyramidal  | 4mm  | C4v | *44  | [4]  | polar | diaboleite | P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc  | I4mm, I4cm, I41md, I41cd
111–122  | Tetragonal scalenohedral  | 42m  | D2d (Vd)  | 2*2  | [2+,4]  |  | chalcopyrite, stannite | P42m, P42c, P421m, P421c, P4m2, P4c2, P4b2, P4n2  | I4m2, I4c2, I42m, I42d
123–142  | Ditetragonal dipyramidal  | 4/mmm  | D4h | *224  | [2,4]  | centrosymmetric  | rutile, pyrolusite, zircon | P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P42/mmc, P42/mcm, P42/nbc, P42/nnm, P42/mbc, P42/mnm, P42/nmc, P42/ncm  | I4/mmm, I4/mcm, I41/amd, I41/acd

## In two dimensions

Main page: Square lattice

There is only one tetragonal Bravais lattice in two dimensions: the square lattice.

Bravais lattice  | Square

|

Pearson symbol | tp
Unit cell |

## See also

* Bravais lattices
* Crystal system
* Crystal structure
* Point groups

## References

1. ↑ Cubic-to-Tetragonal Transition
2. ↑ Webmineral data
3. ↑ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, ISBN 0-471-80580-7
4. ↑ "The 32 crystal classes". https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm.

## External links

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