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Tetragonal

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Tetragonal

In crystallography, the tetragonal crystal system is one of the 7 lattice point groups. 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).

There are two tetragonal crystal structure types. 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 face-centered tetragonal is equivalent to body-centered tetragonal, BCT (with a smaller lattice spacing). BCT is considered more fundamental, so that is the standard terminology.[1]

Tetragonal Bravais lattices
Primitive Body-centered

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

# Point group Example Space groups
Class Intl Schoenflies Orbifold Coxeter
75-80 Tetragonal pyramidal 4 C4 44 [4]+ pinnoite, richellite P4, P41, P42, P43, I4, I41
81-82 Tetragonal disphenoidal 4 S4 2x [2+,4+] cahnite, tugtupite P4, I4
83-88 Tetragonal dipyramidal 4/m C4h 4* [2,4+] scheelite, wulfenite, leucite P4/m, P42/m, P4/n, P42/n, I4/m, I41/a
89-98 Tetragonal trapezohedral 422 D4 224 [2,4]+ cristobalite, wardite P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212, I422, I4122
99-110 Ditetragonal pyramidal 4mm C4v *44 [4] diaboleite P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc, I4mm, I4cm, I41md, I41cd
111-122 Tetragonal scalenohedral 42m D2d 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] 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

References

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