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of or relating to or shaped like a quadrilateral

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/05/17 07:03:20」(JST)

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An example of the tetragonal crystals, wulfenite

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
Name	Primitive	Body-centered
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					Example	Space groups
#	Class	Intl	Schoen.	Orb.	Cox.	Example	Space groups
75–80	Tetragonal pyramidal	4	C₄	44	[4]⁺	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	C_4h	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	C_4v	*44	[4]	diaboleite	P4mm, P4bm, P4₂cm, P4₂nm, P4cc, P4nc, P4₂mc, P4₂bc I4mm, I4cm, I4₁md, I4₁cd
111–122	Tetragonal scalenohedral	42m	D_2d	2*2	[2⁺,4]	chalcopyrite, stannite	P42m, P42c, P42₁m, P42₁c, P4m2, P4c2, P4b2, P4n2 I4m2, I4c2, I42m, I42d
123–142	Ditetragonal dipyramidal	4/mmm	D_4h	*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

References

^ Cubic-to-Tetragonal Transition
^ Webmineral data
^ Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, ISBN 0-471-80580-7

English Journal

The mechanism of uranium transformation from U(VI) into nano-uramphite by two indigenous Bacillus thuringiensis strains.

Pan X1, Chen Z1, Chen F2, Cheng Y3, Lin Z4, Guan X5.
Journal of hazardous materials.J Hazard Mater.2015 Oct 30;297:313-9. doi: 10.1016/j.jhazmat.2015.05.019. Epub 2015 May 14.
The mechanism of uranium transformation from U(VI) into nano-uramphite by two indigenous Bacillus thuringiensis strains was investigated in the present work. Our data showed that the bacteria isolated from uranium mine possessed highly accumulation ability to U(VI), and the maximum accumulation capa
PMID 26026850

Characterization of sprayed TiO2 on ITO substrates for solar cell applications.

Arunachalam A1, Dhanapandian S2, Manoharan C1, Sridhar R1.
Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.Spectrochim Acta A Mol Biomol Spectrosc.2015 Oct 5;149:904-12. doi: 10.1016/j.saa.2015.05.014. Epub 2015 May 19.
Titanium dioxide (TiO2) thin films had been deposited with various substrate temperatures by spray pyrolysis technique onto ITO substrates. All films exhibited polycrystalline nature with the preferred orientation along (101) plane. At the substrate temperature 450°C, the film favored the formation
PMID 26004100

Cathodoluminescence properties of gadolinium-doped CaMoO4:Eu nanoparticles.

Ramakrishna PV1.
Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.Spectrochim Acta A Mol Biomol Spectrosc.2015 Oct 5;149:312-6. doi: 10.1016/j.saa.2015.04.047. Epub 2015 Apr 24.
Gadolinium (Gd(3+)) doped CaMoO4:Eu nanoparticles were prepared via facile auto-combustion route and annealed at 900°C for ∼4h. X-ray diffraction study confirms the tetragonal scheelite type of CaMoO4 phase. Low voltage cathodoluminescent (CL) measurement were performed for Gd(3+) (0 and 10at.%)
PMID 25965514