Tetragonal crystal system
Tetragonal crystal system
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An example of the tetragonal crystals, wulfenite
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
1.1 Two-dimensional
1.2 Three-dimensional
2 Crystal classes
3 See also
4 References
Bravais lattices[edit]
Two-dimensional[edit]
There is only one tetragonal Bravais lattice in two dimensions: the square lattice.
Three-dimensional[edit]
There are two tetragonal Bravais lattices: the simple tetragonal (from stretching the simple-cubic lattice) and the centered tetragonal (from stretching either the face-centered or the body-centered cubic lattice). One might suppose stretching face-centered cubic would result in face-centered tetragonal, but the face-centered tetragonal is equivalent to the body-centered tetragonal, BCT (with a smaller lattice spacing). BCT is considered more fundamental, and therefore this is the standard terminology.[1]
| Bravais lattice | Primitive tetragonal | Body-centered tetragonal |
|---|---|---|
Pearson symbol | tP | tI |
Unit cell |  |  |
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 |
See also[edit]
- Crystal structure
- Point groups
- Bravais lattices
References[edit]
^ Cubic-to-Tetragonal Transition
^ Webmineral data
^ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
ISBN 0-471-80580-7
^ "The 32 crystal classes". Retrieved 2018-06-19.
The 7 crystal systems | |
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