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).

An example of the tetragonal crystals, wulfenite

Bravais lattices


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


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 the face-centered tetragonal is equivalent to the body-centered tetragonal, BCT (with a smaller lattice spacing). BCT is considered more fundamental, and therefore this is the standard terminology.[1]

Bravais lattice Primitive
Pearson symbol tP tI
Unit cell Tetragonal Tetragonal-body-centered

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 4 C4 44 [4]+ enantiomorphic polar pinnoite,
P4, P41, P42, P43 I4, I41
81–82 Tetragonal disphenoidal 4 S4 [2+,4+] cahnite, tugtupite P4 I4
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 [4] polar diaboleite P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc I4mm, I4cm, I41md, I41cd
111–122 Tetragonal scalenohedral 42m D2d (Vd) 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] 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

See also


  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.

Abernathyite is a mineral with formula K(UO2)(AsO4)·3H2O. The mineral is named after Jesse Evrett Abernathy (1913–1963) who first noted it in 1953 in the U.S. State of Utah. It was described as a new mineral species in 1956. Abernathyite is yellow and occurs as small crystals.


Apophyllite-(KF) or fluorapophyllite is a mineral of the apophyllite group, with the chemical formula of KCa4Si8O20(F,OH)·8(H2O). It gets the first half of its name, "fluor", from containing more fluorine than hydroxide compared to the other minerals in the apophyllite group.

Fluorapophyllite crystallizes in the tetragonal crystal system. Tetragonal minerals have three axes of different lengths and angles of 90 degrees. Fluorapophyllite is an anisotropic mineral and has low relief. This mineral belongs to the uniaxial (+) optical class, which means its indicatrix has a prolate sphenoid shape with a circular section, principal section, and one optic axis.Among the apophyllite group, fluorapophyllite is the most abundant compared to the other two minerals in the group, hydroxyapophyllite and natroapophyllite. It is popular among many mineral collectors because of the large, well-developed crystals they form and the multiple colors they come in. The most wanted variation of fluorapophyllite is the green colored variant, which is found in India. Fluorapophyllite is also found in New Jersey of the United States. This mineral is found as a secondary mineral in vesicules in volcanic rocks such as basalt.


BCT is an abbreviation that can mean:

IATA code for Boca Raton Airport,located in Palm Beach County,Florida

BCTGM, Bakers, confectioners, and Tobacco Workers Union

Baire category theorem, a result from general topology

Baltic Chain Tour, a road bicycle race

Banque Centrale de Tunisie in Tunisia

Basic Cadet Training, initial military training for new cadets at the United States Air Force Academy

Basic Combat Training

Bat Conservation Trust, a British charity

Behavior Change Technique

The Blue Carpet Treatment, an album by Snoop Dogg

Box compression test, a measure in corrugated fiber board packaging design and testing

Brigade Combat Team - the basic deployable unit of maneuver in the United States Army

Broward County Transit, a Fort Lauderdale-based system of public transportation

Buffalo Central Terminal, a railroad station located in Buffalo, New York

Mumbai Central Railway station code

Purple Line (Washington Metro), a proposed addition to the Washington Metrorail (formerly known as the Bi-County Transitway)

BC Transit, The company responsible for public transit in most of British Columbia

Body Centered Tetragonal, a type of crystal structure, see Tetragonal crystal system

Another abbreviation for Best Available Control Technology, used in environmental legislation

Business Chinese Test, part of the three Hanban Institute (HSK, YCT and BCT) Chinese tests; see List of language proficiency tests#Mandarin


Braggite is a sulfide mineral of platinum, palladium and nickel with chemical formula: (Pt, Pd, Ni)S. It is a dense (specific gravity of 10), steel grey, opaque mineral which crystallizes in the tetragonal crystal system. It is the central member in the platinum group end-members cooperite and vysotskite.

It was first described in 1932 for an occurrence in the Bushveld Igneous Complex of South Africa. Its name came from William Henry Bragg (1862–1942) and his son, William Lawrence Bragg (1890–1971). It was the first mineral that was discovered with the assistance of X rays.It occurs as magmatic segregations in layered igneous intrusions such as Bushveld, the Stillwater igneous complex, the Lac des Îles igneous complex, the Isle of Rum intrusive, the Great Dyke and many others. It is one of the most common platinum group minerals.


Chatkalite is a copper, iron, tin sulfide mineral with formula Cu6Fe2+Sn6S8. It crystallizes in the tetragonal crystal system and forms as rounded dissemations within tetrahedrite in quartz veins.


For the iron chromium sulfide mineral see DaubréeliteDaubréeite is a rare bismuth oxohalide mineral with formula BiO(OH,Cl). It is a creamy-white to yellow-brown, soft, earthy clay–like mineral which crystallizes in the tetragonal crystal system. It is a member of the matlockite group.It was first described for an occurrence in the Constanicia mine, Tazna, Bolivia, in 1876. It was named for French mineralogist Gabriel Auguste Daubrée (1814–1896). At the Tanza location it occurs as a secondary mineral formed by the oxidation of native bismuth or bismuthinite. It occurs with clay minerals. In addition to its discovery location it has also been reported from the Tintic District in the East Tintic Mountains of Juab County, Utah; in the Josephine Creek District of Josephine County, Oregon; in the Manhattan District of Nye County, Nevada; and the Rio Marina Mine on Elba, Italy.


Gehlenite, (Ca2Al[AlSiO7]), is a sorosilicate, Al-rich endmember of the melilite complete solid solution series with akermanite.

The type locality is in the Monzoni Mountains, Fassa Valley in Trentino in Italy, and is named after Adolf Ferdinand Gehlen (1775–1815) by A.J. Fuchs in 1815.

Jaejun Yu

Jaejun Yu is a South Korean professor of physics at the Seoul National University.


Mackinawite is an iron nickel sulfide mineral with formula (Fe,Ni)1 + xS (where x = 0 to 0.11). The mineral crystallizes in the tetragonal crystal system and has been described as a distorted, close packed, cubic array of S atoms with some of the gaps filled with Fe. Mackinawite occurs as opaque bronze to grey-white tabular crystals and anhedral masses. It has a Mohs hardness of 2.5 and a specific gravity of 4.17. It was first described in 1962 for an occurrence in the Mackinaw mine, Snohomish County, Washington for which it was named.


Maucherite is a grey to reddish silver white nickel arsenide mineral. It crystallizes in the tetragonal crystal system. It occurs in hydrothermal veins alongside other nickel arsenide and sulfide minerals. It is metallic and opaque with a hardness of 5 and a specific gravity of 7.83. It is also known as placodine and Temiskamite. The unit cell is of symmetry group P41212 or P43212.

It has the chemical formula: Ni11As8 and commonly contains copper, iron, cobalt, antimony, and sulfur as impurities.

It was discovered in 1913 in Eisleben, Germany and was named after Wilhelm Maucher (1879–1930), a German mineral collector.

Minium (mineral)

Minium is the naturally occurring form of lead tetroxide, Pb2+2Pb4+O4 also known as red lead. Minium is a light-to-vivid red and may have brown-to-yellow tints. It typically occurs in scaly-to-earthy masses. It crystallizes in the tetragonal crystal system.Minium is rare and occurs in lead-mineral deposits that have been subjected to severe oxidizing conditions. It also occurs as a result of mine fires. It is associated with cerussite, galena, litharge, massicot, mimetite, native lead, and wulfenite.It occurs in relatively small amounts throughout the world: Langhecke, Hesse; Badenweiler, Baden-Württemberg; Bleialf, Eifel district; Horhausen (Grube Holzappel), Rhineland-Palatinate in Germany. It occurs at Mies, Slovenia; Leadhills, Lanarkshire, Scotland; Castelberg St. Avold, Moselle, France; from Langban, Varmland, Sweden; Sarrabus, Sardinia, Italy; near Anarak, Iran; and Tsumeb, Namibia. In the US, mines include the Jay Gould mine, Alturas County, Idaho; the Leadville district, Lake County, Colorado; and in the Tonopah-Belmont mine, Maricopa County, Arizona. It also occurs in Eschuchapa and Guerrero, Mexico. Good specimens were produced by a mine fire at the Broken Hill mine in New South Wales, Australia.Minium has been identified as one of the pigments at Angkor Wat in Cambodia. Minium was named for the Iberian river known to the imperial Romans as Minius, now known as the Spanish Miño and the Portuguese Minho. The name was originally applied to certain forms of cinnabar that had been coated with the minium oxide; however, once the red lead contaminant was determined to be chemically distinct from cinnabar crystals, the name, minium, was applied.For properties and uses of minium see lead tetroxide.


Mooihoekite is a copper iron sulfide mineral with chemical formula of Cu9Fe9S16. The mineral was discovered in 1972 and received its name from its discovery area, the Mooihoek mine in Transvaal, South Africa.


Pinnoite is a magnesium borate mineral with formula: MgB2O(OH)6 or MgB2O4·3(H2O). It crystallizes in the tetragonal crystal system and occurs as colorless to yellow or light green radial fibrous clusters and rarely as short prismatic crystals.

Pinnoite was first described in 1884 for an occurrence in the Stassfurt potash deposit, Saxony-Anhalt, Germany and named for the mine counselor Oberbergrat Pinno of Halle, Germany. It occurs in marine evaporite deposits and as efflorescence associated with mineral springs. It occurs with boracite and kaliborite. It also occurs in the borax mines of Death Valley in California, the Da

Quidam saline lake of the Qinghai-Xizang Plateau in Tibet and in Socacastro, Salta Province, Argentina.


Sellaite is a magnesium fluoride mineral with the formula MgF2. It crystallizes in the tetragonal crystal system typically as clear to white vitreous prisms. It may be fibrous and occur as radiating aggregates. It has a Mohs hardness of 5 to 6 and a specific gravity of 2.97 to 3.15. Refractive index values are nω = 1.378 and nε = 1.390.


Stolzite is a mineral, a lead tungstate; with the formula PbWO4. It is similar to, and often associated with, wulfenite which is the same chemical formula except that the tungsten is replaced by molybdenum. Stolzite crystallizes in the tetragonal crystal system and is dimorphous with the monoclinic form raspite.Lead tungstate crystals have the optical transparency of glass combined with much higher density (8.28 g/cm3 vs ~2.2 g/cm3 for fused silica). They are used as scintillators in particle physics because of their short radiation length (0.89 cm), low Molière radius (2.2 cm), quick scintillation response, and radiation hardness. Lead tungstate crystals are used in the Compact Muon Solenoid's electromagnetic calorimeter.It was first described in 1820 by August Breithaupt, who called it Scheelbleispath and then by François Sulpice Beudant in 1832, who called it scheelitine. In 1845, Wilhelm Karl Ritter von Haidinger coined the name stolzite for an occurrence in Krusne Hory (Erzgebirge), Czech Republic, naming it after Joseph Alexi Stolz of Teplice in Bohemia. It occurs in oxidized hydrothermal tungsten-lead ore deposits typically in association with raspite, cerussite, anglesite, pyromorphite and mimetite.


Wakefieldite ((La,Ce,Nd,Y)VO4) is an uncommon rare-earth element vanadate mineral. There are four main types of wakefieldite- wakefieldite-(La), wakefieldite-(Ce), wakefieldite-(Nd), and wakefieldite-(Y), depending upon the dominant rare-earth metal ion present. Wakefieldite has a Mohs hardness ranging from 4 to 5. Wakefieldite forms crystals of tetragonal structure. In terms of crystal structure, it is the vanadate analog of the rare-earth phosphate mineral xenotime. Unlike xenotime, it is more favorable for wakefieldite to contain the lighter rare-earth elements over the heavier ones. Due to the lanthanide contraction, the heavier rare earths have smaller ionic radii than the lighter ones. When the phosphate anion is replaced by the larger vanadate anion, the tetragonal crystal system preferentially accommodates the larger light rare-earth elements.Wakefieldite was first described for an occurrence in the Evans Lou mine, St. Pierre de Wakefield, Quebec, Canada and later designated Wakefieldite-(Y).Wakefieldite-(Ce) was first described as kusuite for its type locality in the Kusu deposit, 85 km (53 mi) SW of Kinshasa, Zaire. It was renamed in 1977 as the Ce analog of wakefieldite-Y.Wakefieldite-(La) was first described in 2008 for an occurrence in the Glücksstern mine, Gottlob Hill, Friedrichroda, Thuringia, Germany.Wakefieldite-(Nd) was first described in 2008 at the Arase mine, Kami city, Kōchi Prefecture, Shikoku Island, Japan.

Yttrium oxyfluoride

Yttrium oxyfluoride is an inorganic chemical compound with the formula YOF. Under normal conditions, the compound is a colorless solid.


Zircon ( or ) is a mineral belonging to the group of nesosilicates. Its chemical name is zirconium silicate, and its corresponding chemical formula is ZrSiO4. A common empirical formula showing some of the range of substitution in zircon is (Zr1–y, REEy)(SiO4)1–x(OH)4x–y. Zircon forms in silicate melts with large proportions of high field strength incompatible elements. For example, hafnium is almost always present in quantities ranging from 1 to 4%. The crystal structure of zircon is tetragonal crystal system. The natural color of zircon varies between colorless, yellow-golden, red, brown, blue and green. Colorless specimens that show gem quality are a popular substitute for diamond and are also known as "Matura diamond".

The name derives from the Persian zargun, meaning "gold-hued". This word is corrupted into "jargoon", a term applied to light-colored zircons. The English word "zircon" is derived from Zirkon, which is the German adaptation of this word. Yellow, orange and red zircon is also known as "hyacinth", from the flower hyacinthus, whose name is of Ancient Greek origin.


Åkermanite (Ca2Mg[Si2O7]) is a melilite mineral of the sorosilicate group, containing calcium, magnesium, silicon, and oxygen. It is a product of contact metamorphism of siliceous limestones and dolostones, and rocks of sanidinite facies. Sanidinite facies represent the highest conditions of temperature of contact metamorphism and are characterized by the absence of hydrous minerals. It has a density of 2.944 g/cm3. Åkermanite ranks a 5 or 6 on the Mohs scale of mineral hardness, and can be found gray, green, brown, or colorless. It has a white streak and a vitreous or resinous luster. It has a tetragonal crystal system and a good, or distinct, cleavage. It is the end member in a solid solution series beginning with gehlenite (Ca2Al[AlSiO2]).The mineral is named for Anders Richard Åkerman (1837–1922), a Swedish metallurgist. It has been found at Monte Somma and Vesuvius, and Monte Cavalluccio near Rome. It was "grandfathered" in as a species of mineral because it was described prior to 1959, before the founding of the International Mineralogical Association.

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