Tetragonal crystal system

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).

Bravais lattices

Two-dimensional

There is only one tetragonal Bravais lattice in two dimensions: the square lattice.

Three-dimensional

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 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]

Bravais lattice Primitive
tetragonal		 Body-centered
tetragonal
Pearson symbol tP tI
Unit cell

Crystal classes

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 4C444[4]+ enantiomorphic polar pinnoite,
piypite		 P4, P41, P42, P43I4, I41
81–82 Tetragonal disphenoidal 4S42×[2+,4+] cahnite, tugtupite P4I4
83–88 Tetragonal dipyramidal 4/mC4h4*[2,4+] centrosymmetric scheelite, wulfenite, leucite P4/m, P42/m, P4/n, P42/nI4/m, I41/a
89–98 Tetragonal trapezohedral 422D4224[2,4]+ enantiomorphic cristobalite, wardite P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212I422, I4122
99–110 Ditetragonal pyramidal 4mmC4v*44[4] polar diaboleite P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bcI4mm, I4cm, I41md, I41cd
111–122 Tetragonal scalenohedral 42mD2d (Vd)2*2[2+,4] chalcopyrite, stannite P42m, P42c, P421m, P421c, P4m2, P4c2, P4b2, P4n2I4m2, I4c2, I42m, I42d
123–142 Ditetragonal dipyramidal 4/mmmD4h*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/ncmI4/mmm, I4/mcm, I41/amd, I41/acd

See also

References

  1. ↑ Cubic-to-Tetragonal Transition
  2. ↑ Webmineral data
  3. ↑ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, ISBN 0-471-80580-7
  4. ↑ "The 32 crystal classes". Retrieved 2018-06-19.
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