In crystallography, the tetragonal crystal system is one of the seven 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

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

Bravais lattice Primitivetetragonal Body-centeredtetragonal Pearson symbol tP tI Unit cell

The face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell,Cubic-to-Tetragonal Transition while the base-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell.Certain Types of Non-Primitive Lattices Aren't Considered

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.Webmineral dataHurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78,

# Point group Type Example Space groupsName Intl Schoen. Orb. Cox. Primitive Body-centered 75–80 Tetragonal pyramidal 4 C4 44 + enantiomorphic polar pinnoite, piypite P4, P41, P42, P43 I4, I41 81–82 Tetragonal disphenoidal S4 2× [2+,4+] cahnite, tugtupite P I 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 polar diaboleite P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc I4mm, I4cm, I41md, I41cd 111–122 Tetragonal scalenohedral 2m D2d (Vd) 2*2 [2+,4] chalcopyrite, stannite P2m, P2c, P21m, P21c, Pm2, Pc2, Pb2, Pn2 Im2, Ic2, I2m, I2d 123–142 Ditetragonal dipyramidal 4/mmm (4/m 2/m 2/m) 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

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

Bravais lattice Square Pearson symbol tp Unit cell

See also Bravais lattices Crystal system Crystal structure Point groups

References

External links