Tetragonal crystal system
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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 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 (4/m 2/m 2/m) | 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
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- ^ Cubic-to-Tetragonal Transition
- ^ Webmineral data
- ^ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, Template:Isbn
- ^ Page Module:Citation/CS1/styles.css has no content."The 32 crystal classes". Retrieved 2018-06-19.
External links
- Page Template:Sister-inline/styles.css has no content.Script error: No such module "Sister project logo". Media related to Script error: No such module "Commons link". at Wikimedia Commons
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