Tetragonal crystal system

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An example of the tetragonal crystals, wulfenite WulfeniteUSGOV.jpg
An example of the tetragonal crystals, wulfenite
Two different views (top down and from the side) of the unit cell of tP30-CrFe (s-phase Frank-Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system. TP30-CrFe crystalmaker.pdf
Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system.

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

Bravais lattices

There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal.

Bravais latticePrimitive
tetragonal
Body-centered
tetragonal
Pearson symbol tPtI
Unit cell Tetragonal.svg Body-centered tetragonal.svg

The base-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

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 groupTypeExample Space groups
Name [4] Intl Schoen. Orb. Cox. PrimitiveBody-centered
75–80Tetragonal pyramidal4C444[4]+ enantiomorphic polar pinnoite,
piypite
P4, P41, P42, P43I4, I41
81–82Tetragonal disphenoidal4S4[2+,4+] cahnite, tugtupite P4I4
83–88Tetragonal dipyramidal4/mC4h4*[2,4+] centrosymmetric scheelite, wulfenite, leucite P4/m, P42/m, P4/n, P42/nI4/m, I41/a
89–98Tetragonal trapezohedral422D4224[2,4]+ enantiomorphic cristobalite, wardite P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212I422, I4122
99–110Ditetragonal pyramidal4mmC4v*44[4] polar diaboleite P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bcI4mm, I4cm, I41md, I41cd
111–122Tetragonal scalenohedral42mD2d (Vd)2*2[2+,4] chalcopyrite, stannite P42m, P42c, P421m, P421c, P4m2, P4c2, P4b2, P4n2I4m2, I4c2, I42m, I42d
123–142Ditetragonal dipyramidal4/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

In two dimensions

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

Bravais latticeSquare
Pearson symbol tp
Unit cell 2d tp.svg

See also

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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.