Tetragonal crystal system: Difference between revisions
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[[File:WulfeniteUSGOV.jpg|thumb|right|200px|An example of | [[File:WulfeniteUSGOV.jpg|thumb|right|200px|An example of tetragonal crystals, [[wulfenite]]]] | ||
[[File:TP30-CrFe crystalmaker.pdf|thumb|right|300px|Two different views (top down and from the side) of the unit cell of ''tP''30-CrFe (σ-phase [[Frank–Kasper phases|Frank–Kasper structure]]) that show its different side lengths, making this structure a member of the tetragonal crystal system.]] | [[File:TP30-CrFe crystalmaker.pdf|thumb|right|300px|Two different views (top down and from the side) of the unit cell of ''tP''30-CrFe (σ-phase [[Frank–Kasper phases|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 | In [[crystallography]], the '''tetragonal crystal system''' is one of the seven [[crystal system]]s. Tetragonal [[crystal lattice]]s result from stretching a cubic lattice along one of its lattice vectors, so that the [[Cube (geometry)|cube]] becomes a rectangular [[Prism (geometry)|prism]] with a square base (''a'' by ''a'') and height (''c'', which is different from ''a''). | ||
== Bravais lattices == | == Bravais lattices == | ||
Latest revision as of 17:48, 17 June 2025
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In crystallography, the tetragonal crystal system is one of the seven 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).
Bravais lattices
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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 | File:Tetragonal.svg | File:Body-centered tetragonal.svg |
The body-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
Script error: No such module "labelled list hatnote". 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
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| Bravais lattice | Square |
|---|---|
| Pearson symbol | tp |
| Unit cell | File:2d tp.svg |
See also
References
External links
Template:Crystal systems Template:Authority control
- ↑ Cubic-to-Tetragonal Transition
- ↑ Webmineral data
- ↑ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, Template:Isbn
- ↑ Script error: No such module "citation/CS1".