This article needs additional citations for verification. (July 2011) |
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).
Bravais lattices edit
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 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 edit
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 edit
There is only one tetragonal Bravais lattice in two dimensions: the square lattice.
Bravais lattice | Square |
---|---|
Pearson symbol | tp |
Unit cell |
See also edit
References edit
- ^ Cubic-to-Tetragonal Transition
- ^ Webmineral data
- ^ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, ISBN 0-471-80580-7
- ^ "The 32 crystal classes". Retrieved 2018-06-19.
External links edit
- Media related to Tetragonal lattices at Wikimedia Commons