Editing Cubic crystal system

{{short description|Crystallographic system where the unit cell is in the shape of a cube}}
[[File:Pyrite_Cubes.JPG|thumb|right|200px|A rock containing three crystals of [[pyrite]] (FeS<sub>2</sub>). The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural [[facet|crystal facets]].]]
[[File:Kubisches_Kristallsystem.jpg|thumb|right|200px|A network model of a primitive cubic system]]
[[File:FCC_primative-cubic_cells.svg|thumb|right|200px|The primitive and cubic close-packed (also known as face-centered cubic) unit cells]]
In [[crystallography]], the '''cubic''' (or '''isometric''') '''crystal system''' is a [[crystal system]] where the [[Crystal structure#Unit cell|unit cell]] is in the shape of a [[cube]]. This is one of the most common and simplest shapes found in [[crystal]]s and [[mineral]]s.

There are three main varieties of these crystals:
*'''Primitive cubic''' (abbreviated ''cP'' and alternatively called '''simple cubic''')
*'''Body-centered cubic''' (abbreviated ''cI'' or '''bcc''')
*'''Face-centered cubic''' (abbreviated ''cF'' or '''fcc''')
Note: the term '''fcc''' is often used in synonym for the [[Close-packing of equal spheres|''cubic close-packed'']] or '''ccp''' structure occurring in metals. However, '''fcc''' stands for a face-centered cubic Bravais lattice, which is not necessarily close-packed when a motif is set onto the lattice points. E.g. the diamond and the zincblende lattices are '''fcc''' but not close-packed.
Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the [[primitive cell|primitive unit cell]]s often are not.

==Bravais lattices==
{{further information|Bravais lattice}}
The three Bravais latices in the cubic crystal system are:

{| class="wikitable skin-invert-image"
! Bravais lattice
! Primitive<br/>cubic
! Body-centered<br/>cubic
! Face-centered<br/>cubic
|- align=center
! [[Pearson symbol]]
| ''cP''
| ''cI''
| ''cF''
|-
! [[Crystal structure#Unit cell|Unit cell]]
| [[File:Cubic.svg|100px]]
| [[File:Cubic-body-centered.svg|100px]]
| [[File:Cubic-face-centered.svg|100px]]
|}

The primitive cubic lattice (cP) consists of one [[Lattice (group)|lattice]] point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom ({{frac|8}}&nbsp;×&nbsp;8).<ref name=IUCnames>{{cite journal|title=Nomenclature for crystal families, Bravais-lattice types and arithmetic classes. Report of the International Union of Crystallography Ad-Hoc Committee on the Nomenclature of Symmetry|year=1985|journal=[[Acta Crystallographica Section A]]|volume=41|issue=3|page=278|doi=10.1107/S0108767385000587|doi-access=free|last1=De Wolff |first1=P. M. |last2=Belov |first2=N. V. |last3=Bertaut |first3=E. F. |last4=Buerger |first4=M. J. |last5=Donnay |first5=J. D. H. |last6=Fischer |first6=W. |last7=Hahn |first7=Th. |last8=Koptsik |first8=V. A. |last9=MacKay |first9=A. L. |last10=Wondratschek |first10=H. |last11=Wilson |first11=A. J. C. |last12=Abrahams |first12=S. C. }}</ref>

The body-centered cubic lattice (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of two lattice points per unit cell ({{frac|8}}&nbsp;×&nbsp;8 +&nbsp;1).<ref name=IUCnames />

The face-centered cubic lattice (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of four lattice points per unit cell ({{frac|8}}&nbsp;×&nbsp;8 from the corners plus {{frac|2}}&nbsp;×&nbsp;6 from the faces).

The face-centered cubic lattice is closely related to the [[Hexagonal crystal system|hexagonal close packed]] (hcp) system, where two systems differ only in the relative placements of their hexagonal layers. The [[Miller index|[111]]] plane of a face-centered cubic lattice is a hexagonal grid.

Attempting to create a base-centered cubic lattice (i.e., putting an extra lattice point in the center of each horizontal face) results in a simple [[Tetragonal crystal system|tetragonal]] [[Bravais lattice]].

[[Coordination number]] (CN) is the number of nearest neighbors of a central atom in the structure.<ref name=IUCnames /> Each sphere in a cP lattice has coordination number 6, in a cI lattice 8, and in a cF lattice 12.

[[Atomic packing factor]] (APF) is the fraction of volume that is occupied by atoms. The cP lattice has an APF of about 0.524, the cI lattice an APF of about 0.680, and the cF lattice an APF of about 0.740.

==Crystal classes==
{{further information|Crystallographic point group}}
The ''isometric crystal system'' class names, point groups (in [[Schoenflies notation|Schönflies notation]], [[Hermann–Mauguin notation]], [[orbifold]], and [[Coxeter notation]]), type, examples, international tables for crystallography space group number,<ref name="ITC">{{cite book |title=International Tables for Crystallography |doi=10.1107/97809553602060000001 |isbn=978-1-4020-4969-9 |editor-first=E. |editor-last=Prince |year=2006 |s2cid=146060934 }}</ref> and [[space group]]s are listed in the table below. There are a total 36 cubic space groups.

{| class=wikitable
|-
! rowspan=2| No.
! colspan=5| Point group
! rowspan=2| Type
! rowspan=2| Example
! colspan=3| [[Space group]]s
|- align=center
! Name<ref name=Webmin>[http://webmineral.com/crystall.shtml ''Crystallography and Minerals Arranged by Crystal Form''], Webmineral</ref>
! [[Schoenflies notation|Schön.]]
! [[Hermann–Mauguin notation|Intl]]
! [[Orbifold|Orb.]]
! [[Coxeter notation|Cox.]]
! Primitive
! Face-centered
! Body-centered
|- align=center
! <small>195–197</small>
| rowspan=2| Tetartoidal
| rowspan=2| [[Tetrahedral symmetry#Chiral tetrahedral symmetry|T]]
| rowspan=2| 23
| rowspan=2| 332
| rowspan=2| [3,3]<sup>+</sup>
| rowspan=2| [[Chirality (chemistry)|enantiomorphic]]
| rowspan=2| [[Ullmannite]], [[Sodium chlorate]]
| P23
| F23
| I23
|- align=center
! <small>198–199</small>
| [[Ullmannite|P2<sub>1</sub>3]]
|
| I2<sub>1</sub>3
|-  bgcolor=#f4f4f4 align=center
! <small>200–204</small>
| rowspan=2| Diploidal
| rowspan=2| [[Tetrahedral symmetry#Pyritohedral symmetry|T<sub>h</sub>]]
| rowspan=2| 2/m{{overline|3}}<br />(m{{overline|3}})
| rowspan=2| 3*2
| rowspan=2| [3<sup>+</sup>,4]
| rowspan=2| [[Centrosymmetry|centrosymmetric]]
| rowspan=2| [[Pyrite]]
| [[#Caesium chloride structure|Pm{{overline|3}}]], Pn{{overline|3}}
| Fm{{overline|3}}, Fd{{overline|3}}
| I{{overline|3}}
|-  bgcolor=#f4f4f4 align=center
! <small>205–206</small>
| [[Pyrite|Pa{{overline|3}}]]
| 
| Ia{{overline|3}}
|-  align=center
! <small>207–211</small>
| rowspan=2| Gyroidal
| rowspan=2| [[Octahedral symmetry|O]]
| rowspan=2| 432
| rowspan=2| 432
| rowspan=2| [3,4]<sup>+</sup>
| rowspan=2| [[Chirality (chemistry)|enantiomorphic]]
| rowspan=2| [[Petzite]]
| [[Petzite|P432]], P4<sub>2</sub>32
| F432, F4<sub>1</sub>32
| I432
|-  align=center
! <small>212–214</small>
| P4<sub>3</sub>32, P4<sub>1</sub>32
|
| I4<sub>1</sub>32
|-  bgcolor=#f4f4f4 align=center
! <small>215–217</small>
| rowspan=2| Hextetrahedral
| rowspan=2| [[Tetrahedral symmetry#Achiral tetrahedral symmetry|T<sub>d</sub>]]
| rowspan=2| {{overline|4}}3m
| rowspan=2| *332
| rowspan=2| [3,3]
| rowspan=2|
| rowspan=2| [[Sphalerite]]
| P{{overline|4}}3m
| [[#Zincblende structure|F{{overline|4}}3m]]
| I{{overline|4}}3m
|-  bgcolor=#f4f4f4 align=center
! <small>218–220</small>
| P{{overline|4}}3n
| F{{overline|4}}3c
| I{{overline|4}}3d
|- align=center
! <small>221–230</small>
| Hexoctahedral{{anchor|hexoctahedral_link}}
| [[Octahedral symmetry|O<sub>h</sub>]]
| 4/m{{overline|3}}2/m<br />(m{{overline|3}}m)
| *432
| [3,4]
| [[Centrosymmetry|centrosymmetric]]
| [[Galena]], [[Halite]]
| align=left| Pm{{overline|3}}m, Pn{{overline|3}}n, [[#Weaire–Phelan structure|Pm{{overline|3}}n]], Pn{{overline|3}}m
| [[#Rock-salt structure|Fm{{overline|3}}m]], Fm{{overline|3}}c, Fd{{overline|3}}m, Fd{{overline|3}}c
| Im{{overline|3}}m, Ia{{overline|3}}d
|}

Other terms for hexoctahedral are: normal class, [[wiktionary:holohedral|holohedral]], ditesseral central class, [[galena]] type.

==Single element structures==
[[File:visualisation_diamond_cubic.svg|thumb|upright|Visualisation of a diamond cubic unit cell: 1. Components of a unit cell, 2. One unit cell, 3. A lattice of 3 x 3 x 3 unit cells]]
{{See also|Periodic table (crystal structure)}}
As a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the [[Orbital hybridisation|orbital hybridization]] demands certain [[Molecular geometry|bond angles]].) Accordingly, the primitive cubic structure, with especially low atomic packing factor, is rare in nature, but is found in [[polonium]].<ref>{{Greenwood&Earnshaw}}</ref><ref>The original discovery was in J. Chem. Phys. '''14''', 569 (1946).</ref> The ''bcc'' and ''fcc'', with their higher densities, are both quite common in nature. Examples of ''bcc'' include [[iron]], [[chromium]], [[tungsten]], and [[niobium]]. Examples of ''fcc'' include [[aluminium]], [[copper]], [[gold]] and [[silver]].

Another important cubic crystal structure is the [[diamond cubic]] structure, which can appear in [[carbon]], [[silicon]], [[germanium]], and [[tin]]. Unlike fcc and bcc, this structure is not a lattice, since it contains multiple atoms in its [[primitive cell]]. Other cubic elemental structures include the [[A15 phases|A15 structure]] found in [[tungsten]], and the extremely complicated structure of [[manganese]].

==Multi-element structures==
Compounds that consist of more than one element (e.g. [[binary compound]]s) often have crystal structures based on the cubic crystal system. Some of the more common ones are listed here. These structures can be viewed as two or more interpenetrating sublattices where each sublattice occupies the [[interstitial site]]s of the others.

===Caesium chloride structure===
{{Category see also|Caesium chloride crystal structure}}
[[File:CsCl crystal.svg|thumb|left|upright|A [[caesium chloride]] unit cell. The two colors of spheres represent the two types of atoms.]]

One structure is the "interpenetrating primitive cubic" structure, also called a "caesium chloride" or B2 structure. This structure is often confused for a body-centered cubic structure because the arrangement of atoms is the same. However, the caesium chloride structure has a basis composed of two different atomic species. In a body-centered cubic structure, there would be translational symmetry along the [111] direction. In the caesium chloride structure, translation along the [111] direction results in a change of species. The structure can also be thought of as two separate simple cubic structures, one of each species, that are superimposed within each other. The corner of the chloride cube is the center of the caesium cube, and vice versa.<ref name=":2">{{Cite web|title=Cubic Lattices and Close Packing|date=3 October 2013|url=https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_Chem1_(Lower)/07%3A_Solids_and_Liquids/7.08%3A_Cubic_Lattices_and_Close_Packing|url-status=live|archive-url=https://web.archive.org/web/20201101010927/https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_Chem1_(Lower)/07%3A_Solids_and_Liquids/7.08%3A_Cubic_Lattices_and_Close_Packing |archive-date=2020-11-01 }}</ref> 
[[File:Cesium_Chloride.jpg|thumb|This graphic shows the interlocking simple cubic lattices of cesium and chlorine.  You can see them separately and as they are interlocked in what looks like a body-centered cubic arrangement]]

It works the same way for the NaCl structure described in the next section.&nbsp; If you take out the Cl atoms, the leftover Na atoms still form an FCC structure, not a simple cubic structure.

In the unit cell of CsCl, each ion is at the center of a cube of ions of the opposite kind, so the [[coordination number]] is eight. The central cation is coordinated to 8 anions on the corners of a cube as shown, and similarly, the central anion is coordinated to 8 cations on the corners of a cube. Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its [[interstitial site|cubic void]].

In addition to caesium chloride itself, the structure also appears in certain other [[Alkali metal halide|alkali halides]] when prepared at low temperatures or high pressures.<ref name=Seitz>Seitz, ''Modern Theory of Solids'' (1940), p.49</ref> Generally, this structure is more likely to be formed from two elements whose ions are of roughly the same size (for example, ionic radius of Cs<sup>+</sup> = 167 pm, and Cl<sup>−</sup> = 181 pm).

The [[space group]] of the [[caesium chloride]] (CsCl) structure is called Pm{{overline|3}}m (in [[Hermann–Mauguin notation]]), or "221" (in the International Tables for Crystallography). The [[Strukturbericht designation]] is "B2".<ref>[http://cst-www.nrl.navy.mil/lattice/struk/b2.html The CsCl (B2) Structure] {{webarchive|url=https://web.archive.org/web/20080915132850/http://cst-www.nrl.navy.mil/lattice/struk/b2.html|date=2008-09-15}}</ref>

There are nearly a hundred [[Rare-earth element|rare earth]] [[intermetallic compounds]] that crystallize in the CsCl structure, including many [[Binary phase|binary compounds]] of rare earths with [[magnesium]],<ref>{{cite journal | last1=Saccone | first1=A. | last2=Delfino | first2=S. | last3=Macció | first3=D. | last4=Ferro | first4=R. | title=Magnesium-rare earth phase diagrams: Experimental investigation of the Ho-Mg system | journal=Journal of Phase Equilibria 
 | volume=14 | issue=3 | year=1993 | doi=10.1007/bf02668225 | pages=280–287| s2cid=95011597 }}</ref> and with elements in groups [[Group 11 element|11]], [[Group 12 element|12]],<ref>{{cite journal | last1=Kanematu | first1=K | last2=T. Alfieri | first2=G. | last3=Banks | first3=E. | title=Magnetic Studies of Rare Earth Zinc Compounds with CsCl Structure | journal=Journal of the Physical Society of Japan 
| volume=26 | issue=2 | year=1969 | doi=10.1143/jpsj.26.244 | pages=244–248| bibcode=1969JPSJ...26..244K }}</ref><ref>{{cite journal | last=Buschow | first=K. H. J. | title=Magnetic properties of CsCl‐type rare‐earth cadmium compounds | journal=The Journal of Chemical Physics | 
volume=61 | issue=11 | year=1974| doi=10.1063/1.1681788 | pages=4666–4670| bibcode=1974JChPh..61.4666B }}</ref> and [[Group 13 element|13]]. Other compounds showing caesium chloride like structure are [[Cesium bromide|CsBr]], [[Cesium iodide|CsI]], high-temperature [[Rubidium chloride|RbCl]], AlCo, AgZn, BeCu, MgCe, RuAl and SrTl.{{citation needed|date=July 2015}}

===Rock-salt structure===
{{Category see also|Rock salt crystal structure}}
[[File:NaCl octahedra in crystal.svg|thumb|The rock-salt crystal structure. Each atom has six nearest neighbours, with [[octahedral geometry]].]]

The [[space group]] of the rock-salt or [[halite]] (sodium chloride) structure is denoted as Fm{{overline|3}}m (in [[Hermann–Mauguin notation]]), or "225" (in the International Tables for Crystallography). The [[Strukturbericht designation]] is "B1".<ref>[http://cst-www.nrl.navy.mil/lattice/struk/b1.html The NaCl (B1) Structure] {{webarchive|url=https://web.archive.org/web/20081019204213/http://cst-www.nrl.navy.mil/lattice/struk/b1.html |date=2008-10-19 }}</ref>

In the rock-salt  structure, each of the two atom types forms a separate face-centered cubic lattice, with the two lattices interpenetrating so as to form a 3D checkerboard pattern. The rock-salt structure has [[octahedron|octahedral]] [[coordination number|coordination]]: Each atom's nearest neighbors consist of six atoms of the opposite type, positioned like the six vertices of a [[Octahedron#Regular octahedron|regular octahedron]]. In sodium chloride there is a 1:1 ratio of sodium to chlorine atoms.  The structure can also be described as an FCC lattice of sodium with chlorine occupying each [[interstitial site|octahedral void]] or vice versa.<ref name=":2" />

Examples of compounds with this structure include sodium chloride itself, along with almost all other alkali halides, and "many divalent metal oxides, sulfides, selenides, and tellurides".<ref name=Seitz/> According to the [[Cation-anion radius ratio|radius ratio rule]], this structure is more likely to be formed if the cation is somewhat smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732).

The interatomic distance (distance between cation and anion, or half the unit cell length ''a'') in some rock-salt-structure crystals are: 2.3&nbsp;Å  (2.3&nbsp;×&nbsp;10<sup>−10</sup>&nbsp;m) for NaF,<ref>{{Cite journal | last1 = Sundquist | first1 = J. J. | last2 = Lin | first2 = C. C. | doi = 10.1088/0022-3719/14/32/016 | title = Electronic structure of the F centre in a sodium fluoride crystal | journal = Journal of Physics C: Solid State Physics | volume = 14 | issue = 32 | pages = 4797–4805 | year = 1981 |bibcode = 1981JPhC...14.4797S }}</ref> 2.8&nbsp;Å for NaCl,<ref>{{cite journal | journal = [[Acta Crystallographica|Acta Crystallogr.]] | year = 1965 | volume = 18 | pages = 926–932 | title = Accuracy of an automatic diffractometer. Measurement of the sodium chloride structure factors | first1 = S. C. | last1 = Abrahams | first2 = J. L. | last2 = Bernstein | doi = 10.1107/S0365110X65002244 | issue = 5 }}</ref> and 3.2&nbsp;Å for SnTe.<ref>{{Cite journal | last1 = Kao | first1 = W. | last2 = Peretti | first2 = E. | doi = 10.1016/0022-5088(70)90174-8 | title = The ternary subsystem Sn4As3-SnAs-SnTe | journal = Journal of the Less Common Metals | volume = 22 | pages = 39–50 | year = 1970 }}</ref> Most of the [[alkali metal]] [[hydride]]s and [[halide]]s have the rock salt structure, though a few have the [[caesium chloride]] structure instead.

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center"
|+ class="nowrap" |[[Alkali metal]] [[hydride]]s and [[halide]]s with the rock salt structure
! scope="col" | 
! scope="col" | Hydrides
! scope="col" | Fluorides
! scope="col" | Chlorides
! scope="col" | Bromides
! scope="col" | Iodides
|-
! scope="row" | Lithium
|[[Lithium hydride]]
|[[Lithium fluoride]]<ref name=Aigs>J. Aigueperse, P. Mollard, D. Devilliers, M. Chemla, R. Faron, R. Romano, J. P. Cuer, "Fluorine Compounds, Inorganic" (section 4) in Ullmann’s Encyclopedia of Industrial Chemistry, Wiley-VCH, Weinheim, 2005. {{doi|10.1002/14356007.a11_307}}.</ref>
|[[Lithium chloride]]
|[[Lithium bromide]]
|[[Lithium iodide]]
|-
! scope="row" | Sodium
|[[Sodium hydride]]
|[[Sodium fluoride]]<ref name=Aigs/>
|[[Sodium chloride]]
|[[Sodium bromide]]
|[[Sodium iodide]]
|-
! scope="row" | Potassium
|[[Potassium hydride]]
|[[Potassium fluoride]]<ref name=Aigs/>
|[[Potassium chloride]]
|[[Potassium bromide]]
|[[Potassium iodide]]
|-
! scope="row" | Rubidium
|[[Rubidium hydride]]
|[[Rubidium fluoride]]
|[[Rubidium chloride]]
|[[Rubidium bromide]]
|[[Rubidium iodide]]
|-
! scope="row" | Caesium
|[[Caesium hydride]]
|[[Caesium fluoride]]
| colspan="3" style="background:lightgrey"|(CsCl structure)
|-
|}

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center"
|+ class="nowrap" |[[Alkaline earth metal]] [[chalcogenide]]s with the rock salt structure
! scope="col" | 
! scope="col" | Oxides
! scope="col" | Sulfides
! scope="col" | Selenides
! scope="col" | Tellurides
! scope="col" | Polonides
|-
!Magnesium
|[[Magnesium oxide]]
|[[Magnesium sulfide]]
|[[Magnesium selenide]]<ref>{{cite journal | last=Broch | first=Einar | title=Präzisionsbestimmungen der Gitterkonstanten der Verbindungen MgO, MgS, MgSe, MnO und MnSe | journal=Zeitschrift für Physikalische Chemie
 | volume=127U | issue=1 | date=1927-06-01 | doi=10.1515/zpch-1927-12724 | pages=446–454| s2cid=100227546 |language=de}}</ref>
|[[Magnesium telluride]]<ref>{{cite journal | last1=Mir | first1=Showkat H. | last2=Jha | first2=Prakash C. | last3=Dabhi | first3=Shweta | last4=Jha | first4=Prafulla K. | title=''Ab initio'' study of phase stability, lattice dynamics and thermodynamic properties of magnesium chalcogenides | journal=Materials Chemistry and Physics | volume=175 | year=2016 | doi=10.1016/j.matchemphys.2016.02.066 | pages=54–61}}</ref>
| style="background:lightgrey"|(NiAs structure)
|-
!Calcium
|[[Calcium oxide]]
|[[Calcium sulfide]]
|[[Calcium selenide]]<ref>{{cite journal | last1=Louail | first1=L. | last2=Haddadi | first2=K. | last3=Maouche | first3=D. | last4=Ali Sahraoui | first4=F. | last5=Hachemi | first5=A. | title=Electronic band structure of calcium selenide under pressure | journal=Physica B: Condensed Matter | volume=403 | issue=18 | year=2008  | doi=10.1016/j.physb.2008.03.009 | pages=3022–3026| bibcode=2008PhyB..403.3022L }}</ref>
|[[Calcium telluride]]
|[[Calcium polonide]]<ref name=Brown2019>{{cite book | last1=Brown | first1=S.A. | last2=Brown | first2=P.L. | title=The Aqueous Chemistry of Polonium and the Practical Application of its Thermochemistry | publisher=Elsevier Science | year=2019 | isbn=978-0-12-819309-9 | url=https://books.google.com/books?id=eTqvDwAAQBAJ&pg=PA25 | page=25}}</ref>
|-
!Strontium
|[[Strontium oxide]]
|[[Strontium sulfide]]
|[[Strontium selenide]]
|[[Strontium telluride]]
|[[Strontium polonide]]<ref name=Brown2019 />
|-
!Barium
|[[Barium oxide]]
|[[Barium sulfide]]
|[[Barium selenide]]
|[[Barium telluride]]
|[[Barium polonide]]<ref name=Brown2019 />
|}

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center"
|+ class="nowrap" |[[Rare-earth element|Rare-earth]]<ref>{{cite book | last=Hulliger | first=F. | title=Handbook on the Physics and Chemistry of Rare Earths | chapter=Chapter 33 Rare earth pnictides | publisher=Elsevier | year=1979 | volume=4 | doi=10.1016/s0168-1273(79)04006-x | pages=153–236| isbn=9780444852168 }}</ref> and [[actinoid]] [[pnictide]]s with the rock salt structure
! scope="col" | 
! scope="col" | Nitrides
! scope="col" | Phosphides
! scope="col" | Arsenides
! scope="col" | Antimonides
! scope="col" | Bismuthides
|-
! Scandium
|[[Scandium nitride]]
|[[Scandium phosphide]]
|[[Scandium arsenide]]<ref>{{cite journal | last1=Gschneidner | first1=K. A. | last2=Calderwood | first2=F. W. | title=The As−Sc (Arsenic-Scandium) system | journal=Bulletin of Alloy Phase Diagrams | volume=7 | issue=4 | year=1986 | doi=10.1007/bf02873011 | pages=348–349}}</ref>
|[[Scandium antimonide]]<ref>{{cite journal | last1=Hayashi | first1=J | last2=Shirotani | first2=I | last3=Hirano | first3=K | last4=Ishimatsu | first4=N | last5=Shimomura | first5=O | last6=Kikegawa | first6=T | title=Structural phase transition of ScSb and YSb with a NaCl-type structure at high pressures | journal=Solid State Communications | volume=125 | issue=10 | year=2003 | doi=10.1016/s0038-1098(02)00889-x | pages=543–546| bibcode=2003SSCom.125..543H }}</ref>
|[[Scandium bismuthide]]<ref>{{cite book | last=Horovitz | first=C.T. | title=Scandium Its Occurrence, Chemistry Physics, Metallurgy, Biology and Technology | publisher=Elsevier Science | year=2012 | isbn=978-0-323-14451-3 | url=https://books.google.com/books?id=q_IhKRBxxHUC&pg=PA273 | page=273}}</ref>
|-
!Yttrium
|[[Yttrium nitride]]
|[[Yttrium phosphide]]
|[[Yttrium arsenide]]<ref name=Ono1970>{{cite journal | last1=Ono | first1=S. | last2=Despault | first2=J.G. | last3=Calvert | first3=L.D. | last4=Taylor | first4=J.B. | title=Rare-earth arsenides | journal=Journal of the Less Common Metals | volume=22 | issue=1 | year=1970  | doi=10.1016/0022-5088(70)90175-x | pages=51–59}}</ref>
|[[Yttrium antimonide]]
|[[Yttrium bismuthide]]<ref>{{cite journal | last1=Schmidt | first1=F.A. | last2=McMasters | first2=O.D. | last3=Lichtenberg | first3=R.R. | title=The yttrium-bismuth alloy system | journal=Journal of the Less Common Metals | volume=18 | issue=3 | year=1969 | doi=10.1016/0022-5088(69)90159-3 | pages=215–220}}</ref>
|-
!Lanthanum
|[[Lanthanum nitride]]<ref name=Natali>{{cite journal | last1=Natali | first1=F. | last2=Ruck | first2=B.J. | last3=Plank | first3=N.O.V. | last4=Trodahl | first4=H.J. | last5=Granville | first5=S. | last6=Meyer | first6=C. | last7=Lambrecht | first7=W.R.L. | title=Rare-earth mononitrides | journal=Progress in Materials Science | volume=58 | issue=8 | year=2013 | doi=10.1016/j.pmatsci.2013.06.002 | pages=1316–1360| arxiv=1208.2410 | s2cid=118566136 }}</ref>
|[[Lanthanum phosphide]]<ref name=Ono>{{cite journal | last1=Ono | first1=S. | last2=Nomura | first2=K. | last3=Hayakawa | first3=H. | title=Syntheses of new rare-earth phosphides | journal=Journal of the Less Common Metals | volume=38 | issue=2–3 | year=1974 |  doi=10.1016/0022-5088(74)90055-1 | pages=119–130}}</ref>
|[[Lanthanum arsenide]]<ref name=Ono1970 />
|[[Lanthanum antimonide]]
|[[Lanthanum bismuthide]]<ref name=Yoshihara>{{cite journal | last1=Yoshihara | first1=K. | last2=Taylor | first2=J.B. | last3=Calvert | first3=L.D. | last4=Despault | first4=J.G. | title=Rare-earth bismuthides | journal=Journal of the Less Common Metals | volume=41 | issue=2 | year=1975| doi=10.1016/0022-5088(75)90038-7 | pages=329–337}}</ref>
|-
!Cerium
|[[Cerium nitride]]<ref name=Natali />
|[[Cerium phosphide]]<ref name=Ono />
|[[Cerium arsenide]]<ref name=Ono1970 />
|[[Cerium antimonide]]
|[[Cerium bismuthide]]<ref name=Yoshihara />
|-
!Praseodymium
|[[Praseodymium nitride]]<ref name=Natali />
|[[Praseodymium phosphide]]<ref name=Ono />
|[[Praseodymium arsenide]]<ref name=Ono1970 />
|[[Praseodymium antimonide]]<ref name=Hayashi>{{cite journal | last1=Hayashi | first1=J. | last2=Shirotani | first2=I. | last3=Tanaka | first3=Y. | last4=Adachi | first4=T. | last5=Shimomura | first5=O. | last6=Kikegawa | first6=T. | title=Phase transitions of LnSb (Ln=lanthanide) with NaCl-type structure at high pressures | journal=Solid State Communications | volume=114 | issue=11 | year=2000 | doi=10.1016/s0038-1098(00)00113-7 | pages=561–565| bibcode=2000SSCom.114..561H }}</ref>
|[[Praseodymium bismuthide]]<ref name=Yoshihara />
|-
!Neodymium
|[[Neodymium nitride]]<ref name=Natali />
|[[Neodymium phosphide]]<ref name=Ono />
|[[Neodymium arsenide]]<ref name=Ono1970 />
|[[Neodymium antimonide]]<ref name=Hayashi />
|[[Neodymium bismuthide]]<ref name=Yoshihara />
|-
!Promethium
|?
|?
|?
|?
|?
|-
!Samarium
|[[Samarium nitride]]<ref name=Natali />
|[[Samarium phosphide]]<ref name=Ono />
|[[Samarium arsenide]]<ref name=Ono1970 />
|[[Samarium antimonide]]<ref name=Hayashi />
|[[Samarium bismuthide]]<ref name=Yoshihara />
|-
!Europium
|[[Europium nitride]]<ref name=Natali />
|[[Europium phosphide]]
|style="background:lightgrey"|(Na<sub>2</sub>O<sub>2</sub> structure)<ref>{{cite journal | last1=Gschneidner | first1=K. A. | last2=Calderwood | first2=F. W. | title=The As−Eu (Arsenic-Europium) system | journal=Bulletin of Alloy Phase Diagrams | volume=7 | issue=3 | year=1986 | doi=10.1007/bf02869009 | pages=279–283}}</ref>
|colspan="2" style="background:lightgrey"|(unstable)<ref name=Taylor1979>{{cite journal | last1=Taylor | first1=J. B. | last2=Calvert | first2=L. D. | last3=Wang | first3=Y. | title=Powder data for some new europium antimonides and bismuthides | journal=Journal of Applied Crystallography | volume=12 | issue=2 | date=1979 | doi=10.1107/s0021889879012309 | pages=249–251}}</ref>
|-
!Gadolinium
|[[Gadolinium nitride]]<ref name=Natali />
|[[Gadolinium phosphide]]
|[[Gadolinium arsenide]]<ref name=Ono1970 />
|[[Gadolinium antimonide]]<ref name=Hayashi />
|[[Gadolinium bismuthide]]<ref name=Yoshihara />
|-
!Terbium
|[[Terbium nitride]]<ref name=Natali />
|[[Terbium phosphide]]
|[[Terbium arsenide]]<ref name=Ono1970 />
|[[Terbium antimonide]]<ref name=Hayashi />
|[[Terbium bismuthide]]<ref name=Yoshihara />
|-
!Dysprosium
|[[Dysprosium nitride]]<ref name=Natali />
|[[Dysprosium phosphide]]
|[[Dysprosium arsenide]]
|[[Dysprosium antimonide]]
|[[Dysprosium bismuthide]]<ref name=Yoshihara />
|-
!Holmium
|[[Holmium nitride]]<ref name=Natali />
|[[Holmium phosphide]]
|[[Holmium arsenide]]<ref name=Ono1970 />
|[[Holmium antimonide]]
|[[Holmium bismuthide]]<ref name=Yoshihara />
|-
!Erbium
|[[Erbium nitride]]<ref name=Natali />
|[[Erbium phosphide]]
|[[Erbium arsenide]]<ref name=Ono1970 />
|[[Erbium antimonide]]
|[[Erbium bismuthide]]<ref name=Yoshihara />
|-
!Thulium
|[[Thulium nitride]]<ref name=Natali />
|[[Thulium phosphide]]
|[[Thulium arsenide]]
|[[Thulium antimonide]]
|[[Thulium bismuthide]]<ref name=Yoshihara />
|-
!Ytterbium
|[[Ytterbium nitride]]<ref name=Natali />
|[[Ytterbium phosphide]]
|[[Ytterbium arsenide]]<ref name=Ono1970 />
|[[Ytterbium antimonide]]
|style="background:lightgrey"|(unstable)<ref>{{cite journal | last=Okamoto | first=H. | title=Bi-Yb (bismuth-ytterbium) | journal=Journal of Phase Equilibria | volume=20 | issue=4 | year=1999 | doi=10.1361/105497199770335640 | pages=453}}</ref><ref>{{cite journal | last1=Duan | first1=Xu | last2=Wu | first2=Fan | last3=Chen | first3=Jia | last4=Zhang | first4=Peiran | last5=Liu | first5=Yang | last6=Yuan | first6=Huiqiu | last7=Cao | first7=Chao | title=Tunable electronic structure and topological properties of LnPn (Ln=Ce, Pr, Sm, Gd, Yb; Pn=Sb, Bi) | journal=Communications Physics | volume=1 | issue=1 | date=2018 | doi=10.1038/s42005-018-0074-8 | page=71| bibcode=2018CmPhy...1...71D |doi-access=free| arxiv=1802.04554 }}</ref>
|-
!Lutetium
|[[Lutetium nitride]]<ref name=Natali />
|[[Lutetium phosphide]]
|[[Lutetium arsenide]]
|[[Lutetium antimonide]]
|[[Lutetium bismuthide]]
|-
!Actinium
|?
|?
|?
|?
|?
|-
!Thorium
|[[Thorium nitride]]<ref name=Kruger1967 />
|[[Thorium phosphide]]<ref name=Kruger1967 />
|[[Thorium arsenide]]<ref name=Kruger1967 />
|[[Thorium antimonide]]<ref name=Kruger1967 />
| style="background:lightgrey"|(CsCl structure)
|-
!Protactinium
|?
|?
|?
|?
|?
|-
!Uranium
|[[Uranium nitride]]<ref name=Kruger1967 />
|[[Uranium monophosphide]]<ref name=Kruger1967 />
|[[Uranium arsenide]]<ref name=Kruger1967 />
|[[Uranium antimonide]]<ref name=Kruger1967 />
|[[Uranium bismuthide]]<ref name=Vogt1995>{{cite journal | last1=Vogt | first1=O. | last2=Mattenberger | first2=K. | title=The magnetism of localized or nearly localized 4f and 5f shells | journal=Journal of Alloys and Compounds | volume=223 | issue=2 | year=1995 | doi=10.1016/0925-8388(94)09005-x | pages=226–236}}</ref>
|-
!Neptunium
|[[Neptunium nitride]]
|[[Neptunium phosphide]]
|[[Neptunium arsenide]]
|[[Neptunium antimonide]]
|[[Neptunium bismuthide]]<ref name=Vogt1995 />
|-
!Plutonium
|[[Plutonium nitride]]<ref name=Kruger1967 />
|[[Plutonium phosphide]]<ref name=Kruger1967 />
|[[Plutonium arsenide]]<ref name=Kruger1967 />
|[[Plutonium antimonide]]<ref name=Kruger1967 />
|[[Plutonium bismuthide]]<ref name=Vogt1995 />
|-
!Americium
|[[Americium nitride]]<ref name=Vogt1995 />
|[[Americium phosphide]]<ref name=Vogt1995 />
|[[Americium arsenide]]<ref name=Vogt1995 />
|[[Americium antimonide]]<ref name=Vogt1995 />
|[[Americium bismuthide]]<ref name=Vogt1995 />
|-
!Curium
|[[Curium nitride]]<ref name=Benedict1993>{{cite book | last1=Benedict | first1=U. | last2=Holzapfel | first2=W.B. | title=Lanthanides/Actinides: Physics I | chapter=Chapter 113 High-pressure studies — Structural aspects | series=Handbook on the Physics and Chemistry of Rare Earths | publisher=Elsevier | year=1993 | volume=17 | doi=10.1016/s0168-1273(05)80030-3 | pages=245–300| isbn=9780444815026 }}</ref>
|[[Curium phosphide]]<ref name=Benedict1993 />
|[[Curium arsenide]]<ref name=Benedict1993 />
|[[Curium antimonide]]<ref name=Benedict1993 />
|[[Curium bismuthide]]<ref name=Benedict1993 />
|-
!Berkelium
|[[Berkelium nitride]]<ref name=Benedict1993 />
|[[Berkelium phosphide]]<ref name=Benedict1993 />
|[[Berkelium arsenide]]<ref name=Benedict1993 />
|?
|[[Berkelium bismuthide]]<ref name=Benedict1993 />
|-
!Californium
|?
|?
|[[Californium arsenide]]<ref name=Benedict1993 />
|?
|[[Californium bismuthide]]<ref name=Benedict1993 />
|}

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center"
|+ class="nowrap" |[[Rare-earth element|Rare-earth]] and [[actinoid]] [[chalcogenide]]s with the rock salt structure
! scope="col" | 
! scope="col" | Oxides
! scope="col" | Sulfides
! scope="col" | Selenides
! scope="col" | Tellurides
! scope="col" | Polonides
|-
!Scandium
|rowspan="8" style="background:lightgrey"|(unstable)<ref name=Leger1981>{{cite journal | last1=Leger | first1=J.M. | last2=Yacoubi | first2=N. | last3=Loriers | first3=J. | title=Synthesis of rare earth monoxides | journal=Journal of Solid State Chemistry | volume=36 | issue=3 | year=1981 | doi=10.1016/0022-4596(81)90436-9 | pages=261–270| bibcode=1981JSSCh..36..261L | doi-access= }}</ref>
|[[Scandium monosulfide]]
|
|
|
|-
!Yttrium
|[[Yttrium monosulfide]]<ref>{{cite journal | last1=Roedhammer | first1=P. | last2=Reichardt | first2=W. | last3=Holtzberg | first3=F. | title=Soft-Mode Behavior in the Phonon Dispersion of YS | journal=Physical Review Letters | volume=40 | issue=7 | date=1978| doi=10.1103/physrevlett.40.465 | pages=465–468| bibcode=1978PhRvL..40..465R }}</ref>
|
|
|
|-
!Lanthanum
|[[Lanthanum monosulfide]]<ref name=Didchenko1963>{{cite journal | last1=Didchenko | first1=R. | last2=Gortsema | first2=F.P. | title=Some electric and magnetic properties of rare earth monosulfides and nitrides | journal=Journal of Physics and Chemistry of Solids | volume=24 | issue=7 | year=1963 | doi=10.1016/0022-3697(63)90062-3 | pages=863–870| bibcode=1963JPCS...24..863D }}</ref>
|
|
|
|-
!Cerium
|[[Cerium monosulfide]]<ref name=Didchenko1963 />
|[[Cerium monoselenide]]<ref name=Smolensky1968>{{cite journal | last1=Smolensky | first1=G. A. | last2=Adamjan | first2=V. E. | last3=Loginov | first3=G. M. | title=Antiferromagnetic Properties of Light Rare Earth Monochalcogenides | journal=Journal of Applied Physics | volume=39 | issue=2 | year=1968 | doi=10.1063/1.2163619 | pages=786–790| bibcode=1968JAP....39..786S }}</ref>
|[[Cerium monotelluride]]<ref name=Smolensky1968 />
|
|-
!Praseodymium
|[[Praseodymium monosulfide]]<ref name=Didchenko1963 />
|[[Praseodymium monoselenide]]<ref name=Smolensky1968 />
|[[Praseodymium monotelluride]]<ref name=Smolensky1968 />
|
|-
!Neodymium
|[[Neodymium monosulfide]]<ref name=Didchenko1963 />
|[[Neodymium monoselenide]]<ref name=Smolensky1968 />
|[[Neodymium monotelluride]]<ref name=Smolensky1968 />
|
|-
!Promethium
|?
|?
|?
|?
|-
!Samarium
|[[Samarium monosulfide]]<ref name=Didchenko1963 />
|[[Samarium monoselenide]]
|[[Samarium monotelluride]]
|[[Samarium monopolonide]]<ref name=Kershner1966>{{cite journal | last1=Kershner | first1=C.J. | last2=DeSando | first2=R.J. | last3=Heidelberg | first3=R.F. | last4=Steinmeyer | first4=R.H. | title=Rare earth polonides | journal=Journal of Inorganic and Nuclear Chemistry | volume=28 | issue=8 | year=1966 | doi=10.1016/0022-1902(66)80054-4 | pages=1581–1588}}</ref>
|-
!Europium
|[[Europium monoxide]]
|[[Europium monosulfide]]<ref name=Didchenko1963 />
|[[Europium monoselenide]]<ref name=Wachter1972>{{cite journal | last=Wachter | first=P. | title=The optical electrical and magnetic properties of the europium chalcogenides and the rare earth pnictides | journal=C R C Critical Reviews in Solid State Sciences | volume=3 | issue=2 | year=1972 | doi=10.1080/10408437208244865 | pages=189–241}}</ref>
|[[Europium monotelluride]]<ref name=Wachter1972 />
|[[Europium monopolonide]]<ref name=Kershner1966 />
|-
!Gadolinium
|rowspan="6" style="background:lightgrey"|(unstable)<ref name=Leger1981 />
|[[Gadolinium monosulfide]]<ref name=Didchenko1963 />
|
|
|
|-
!Terbium
|[[Terbium monosulfide]]<ref name=Didchenko1963 />
|
|
|[[Terbium monopolonide]]<ref name=Kershner1966 />
|-
!Dysprosium
|[[Dysprosium monosulfide]]<ref name=Didchenko1963 />
|
|
|[[Dysprosium monopolonide]]<ref name=Kershner1966 />
|-
!Holmium
|[[Holmium monosulfide]]<ref name=Didchenko1963 />
|
|
|[[Holmium monopolonide]]<ref name=Kershner1966 />
|-
!Erbium
|[[Erbium monosulfide]]<ref name=Didchenko1963 />
|
|
|
|-
!Thulium
|[[Thulium monosulfide]]<ref name=Didchenko1963 />
|
|
|[[Thulium monopolonide]]<ref name=Kershner1966 />
|-
!Ytterbium
|[[Ytterbium monoxide]]
|[[Ytterbium monosulfide]]<ref name=Didchenko1963 />
|
|
|[[Ytterbium monopolonide]]<ref name=Kershner1966 />
|-
!Lutetium
|rowspan="9" style="background:lightgrey"|(unstable)<ref name=Leger1981 /><ref>{{cite book | last=Meyer | first=G | title=Synthesis of Lanthanide and Actinide Compounds | publisher=Springer Netherlands | publication-place=Dordrecht | year=1991 | isbn=978-94-011-3758-4 | oclc=840310000 | page=237}}</ref>
|[[Lutetium monosulfide]]<ref name=Didchenko1963 />
|
|
|[[Lutetium monopolonide]]<ref name=Kershner1966 />
|-
!Actinium
|?
|?
|?
|?
|-
!Thorium
|[[Thorium monosulfide]]<ref name=Kruger1967>{{cite journal | last1=Kruger | first1=O.L. | last2=Moser | first2=J.B. | title=Lattice constants and melting points of actinide-group IVA-VIA compounds with NaCl-type structures | journal=Journal of Physics and Chemistry of Solids | volume=28 | issue=11 | year=1967 | doi=10.1016/0022-3697(67)90257-0 | pages=2321–2325| bibcode=1967JPCS...28.2321K }}</ref>
|[[Thorium monoselenide]]<ref name=Kruger1967 />
| style="background:lightgrey"|(CsCl structure)<ref>{{cite journal | last1=D'Eye | first1=R. W. M. | last2=Sellman | first2=P. G. | title=The thorium–tellurium system | journal=J. Chem. Soc. | year=1954 | doi=10.1039/jr9540003760 | pages=3760–3766}}</ref>
|
|-
!Protactinium
|?
|?
|?
|?
|-
!Uranium
|[[Uranium monosulfide]]<ref name=Kruger1967 />
|[[Uranium monoselenide]]<ref name=Kruger1967 />
|[[Uranium monotelluride]]<ref name=Kruger1967 />
|
|-
!Neptunium
|[[Neptunium monosulfide]]
|[[Neptunium monoselenide]]
|[[Neptunium monotelluride]]
|
|-
!Plutonium
|[[Plutonium monosulfide]]<ref name=Kruger1967 />
|[[Plutonium monoselenide]]<ref name=Kruger1967 />
|[[Plutonium monotelluride]]<ref name=Kruger1967 />
|
|-
!Americium
|[[Americium monosulfide]]<ref name=Vogt1995 />
|[[Americium monoselenide]]<ref name=Vogt1995 />
|[[Americium monotelluride]]<ref name=Vogt1995 />
|
|-
!Curium
|[[Curium monosulfide]]<ref name=Benedict1993 />
|[[Curium monoselenide]]<ref name=Benedict1993 />
|[[Curium monotelluride]]<ref name=Benedict1993 />
|
|}

{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center"
|+ class="nowrap" |[[Transition metal]] [[carbide]]s and [[nitride]]s with the rock salt structure
! scope="col" | 
! scope="col" | Carbides
! scope="col" | Nitrides
|-
!Titanium
|[[Titanium carbide]]
|[[Titanium nitride]]
|-
!Zirconium
|[[Zirconium carbide]]
|[[Zirconium nitride]]
|-
!Hafnium
|[[Hafnium carbide]]
|[[Hafnium nitride]]<ref>{{cite journal | last1=Friedrich | first1=Alexandra | last2=Winkler | first2=Björn | last3=Juarez-Arellano | first3=Erick A. | last4=Bayarjargal | first4=Lkhamsuren | title=Synthesis of Binary Transition Metal Nitrides, Carbides and Borides from the Elements in the Laser-Heated Diamond Anvil Cell and Their Structure-Property Relations | journal=Materials | volume=4 | issue=10 | date=2011 | doi=10.3390/ma4101648 | pages=1648–1692| pmid=28824101 | pmc=5448873 | bibcode=2011Mate....4.1648F | doi-access=free }}</ref>
|-
!Vanadium
|[[Vanadium carbide]]
|[[Vanadium nitride]]
|-
!Niobium
|[[Niobium carbide]]
|[[Niobium nitride]]
|-
!Tantalum
|[[Tantalum carbide]]
|style="background:lightgrey"| (CoSn structure)
|-
!Chromium
|style="background:lightgrey"| (unstable)<ref>{{cite journal | last1=Venkatraman | first1=M. | last2=Neumann | first2=J. P. | title=The C-Cr (Carbon-Chromium) System | journal=Bulletin of Alloy Phase Diagrams | volume=11 | issue=2 | year=1990 | doi=10.1007/bf02841701 | pages=152–159}}</ref>
|[[Chromium nitride]]
|}

Many [[transition metal]] monoxides also have the rock salt structure ([[Titanium(II) oxide|TiO]], [[Vanadium(II) oxide|VO]], [[Chromium(II) oxide|CrO]], [[Manganese(II) oxide|MnO]], [[Iron(II) oxide|FeO]], [[Cobalt(II) oxide|CoO]], [[Nickel(II) oxide|NiO]], [[Cadmium oxide|CdO]]). The early actinoid monocarbides also have this structure ([[Thorium carbide|ThC]], [[Protactinium carbide|PaC]], [[Uranium carbide|UC]], [[Neptunium carbide|NpC]], [[Plutonium carbide|PuC]]).<ref name=Benedict1993 />

===Fluorite structure===
{{main|Fluorite structure}}
{{Category see also|Fluorite crystal structure}}
Much like the rock salt structure, the [[fluorite structure]] (AB<sub>2</sub>) is also an Fm{{overline|3}}m structure but has 1:2 ratio of ions. The anti-fluorite structure is nearly identical, except the positions of the anions and cations are switched in the structure. They are designated [[Wyckoff positions]] 4a and 8c whereas the rock-salt structure positions are 4a and 4b.<ref>{{Cite web|title=Fluorite|url=http://aflow.org/CrystalDatabase/AB2_cF12_225_a_c|website=aflow.org|access-date=2020-05-22}}</ref><ref>{{Cite web|title=Rock Salt|url=http://aflow.org/CrystalDatabase/AB_cF8_225_a_b.html|website=aflow.org|access-date=2020-05-22}}</ref>

===Zincblende structure===
{{Category see also|Zincblende crystal structure}}
[[File:Sphalerite-unit-cell-depth-fade-3D-balls.png|upright|thumb|A zincblende unit cell]]
The [[space group]] of the Zincblende structure is called F{{overline|4}}3m (in [[Hermann–Mauguin notation]]), or 216.<ref>{{cite book|title=Quantum Theory of the Solid State|author=Kantorovich, L. |page=32|url=https://books.google.com/books?id=YoI2-QvDoUAC&pg=PA32|publisher=Springer|year=2004|isbn=1-4020-2153-4}}</ref><ref>[http://img.chem.ucl.ac.uk/sgp/large/216az1.htm Birkbeck College, University of London]</ref> The Strukturbericht designation is "B3".<ref>[https://web.archive.org/web/19981202071024/http://cst-www.nrl.navy.mil/lattice/struk/b3.html The Zincblende (B3) Structure]. Naval Research Laboratory, U.S. </ref>

The Zincblende structure (also written "zinc blende") is named after the mineral zincblende ([[sphalerite]]), one form of [[zinc sulfide]] (β-ZnS). As in the rock-salt structure, the two atom types form two interpenetrating face-centered cubic lattices. However, it differs from rock-salt structure in how the two lattices are positioned relative to one another. The zincblende structure has [[tetrahedron|tetrahedral]] [[coordination number|coordination]]: Each atom's nearest neighbors consist of four atoms of the opposite type, positioned like the four vertices of a [[Tetrahedron#Regular tetrahedron|regular tetrahedron]]. In zinc sulfide the ratio of zinc to sulfur is 1:1.<ref name=":2" /> Altogether, the arrangement of atoms in zincblende structure is the same as [[diamond cubic]] structure, but with alternating types of atoms at the different lattice sites. The structure can also be described as an FCC lattice of zinc with sulfur atoms occupying half of the [[interstitial site|tetrahedral void]]s or vice versa.<ref name=":2" />

Examples of compounds with this structure include zincblende itself, [[lead(II) nitrate]], many compound semiconductors (such as [[gallium arsenide]] and [[cadmium telluride]]), and a wide array of other binary compounds.{{Citation needed|date=June 2021}} The [[boron group]] [[pnictogenide]]s usually have a zincblende structure, though the [[nitride]]s are more common in the [[wurtzite structure]], and their zincblende forms are less well known [[Polymorphism (materials science)|polymorph]]s.<ref>{{cite journal | last1=Wang | first1=L.D. | last2=Kwok | first2=H.S. | title=Cubic aluminum nitride and gallium nitride thin films prepared by pulsed laser deposition | journal=Applied Surface Science | volume=154–155 | year=2000 | issue=1–4 | doi=10.1016/s0169-4332(99)00372-4 | pages=439–443| bibcode=2000ApSS..154..439W }}</ref><ref>{{cite journal | last1=Oseki | first1=Masaaki | last2=Okubo | first2=Kana | last3=Kobayashi | first3=Atsushi | last4=Ohta | first4=Jitsuo | last5=Fujioka | first5=Hiroshi | title=Field-effect transistors based on cubic indium nitride | journal=Scientific Reports | volume=4 | issue=1 | date=2014 | doi=10.1038/srep03951 | page=3951| pmid=24492240 | pmc=3912472 | bibcode=2014NatSR...4E3951O }}</ref>

{| class="wikitable" style="text-align: center"
|+ [[Copper]] [[halide]]s with the zincblende structure
! scope="col" | 
! scope="col" | Fluorides
! scope="col" | Chlorides
! scope="col" | Bromides
! scope="col" | Iodides
|-
!Copper
|[[Copper(I) fluoride]]
|[[Copper(I) chloride]]
|[[Copper(I) bromide]]
|[[Copper(I) iodide]]
|}

{| class="wikitable" style="text-align: center"
|+ [[Beryllium]] and [[Group 12 element|Group 12]] [[chalcogenide]]s with the zincblende structure
! scope="col" | 
! scope="col" | Sulfides
! scope="col" | Selenides
! scope="col" | Tellurides
! scope="col" | Polonides
|-
! Beryllium
| [[Beryllium sulfide]]
| [[Beryllium selenide]]
| [[Beryllium telluride]]
| [[Beryllium polonide]]<ref>{{Greenwood&Earnshaw1st|page=899}}.</ref><ref>{{cite report | last = Moyer | first = Harvey V. | contribution = Chemical Properties of Polonium | pages = 33–96 | title = Polonium | url = http://www.osti.gov/bridge/servlets/purl/4367751-nEJIbm/ | editor-last = Moyer | editor-first = Harvey V. | id = TID-5221 | doi = 10.2172/4367751 | year = 1956 | location = Oak Ridge, Tenn. | publisher = United States Atomic Energy Commission| doi-access = free }}.</ref>
|-
! Zinc
|[[Zinc sulfide]]
|[[Zinc selenide]]
|[[Zinc telluride]]
|[[Zinc polonide]]
|-
!Cadmium
|[[Cadmium sulfide]]
|[[Cadmium selenide]]
|[[Cadmium telluride]]
|[[Cadmium polonide]]
|-
!Mercury
|[[Mercury sulfide]]
|[[Mercury selenide]]
|[[Mercury telluride]]
| –
|}
This group is also known as the [[II-VI semiconductor compound|II-VI]] family of compounds, most of which can be made in both the zincblende (cubic) or [[Wurtzite crystal structure|wurtzite]] (hexagonal) form.

{| class="wikitable" style="text-align: center"
|+ [[Boron group|Group 13]] [[pnictogenide]]s with the zincblende structure
! scope="col" | 
! scope="col" | Nitrides
! scope="col" | Phosphides
! scope="col" | Arsenides
! scope="col" | Antimonides
|-
! scope="row" | Boron
|[[Boron nitride]]*
|[[Boron phosphide]]
|[[Boron arsenide]]
|[[Boron antimonide]]
|-
! scope="row" | Aluminium
|[[Aluminium nitride]]*
|[[Aluminium phosphide]]
|[[Aluminium arsenide]]
|[[Aluminium antimonide]]
|-
! scope="row" | Gallium
|[[Gallium nitride]]*
|[[Gallium phosphide]]
|[[Gallium arsenide]]
|[[Gallium antimonide]]
|-
! scope="row" | Indium
|[[Indium nitride]]*
|[[Indium phosphide]]
|[[Indium arsenide]]
|[[Indium antimonide]]
|}
This group is also known as the '''III-V''' family of compounds.

[[File:Heusler alloy - structure.png|thumb|right| The structure of the [[Heusler compound]]s with formula X<sub>2</sub>YZ (e. g., Co<sub>2</sub>MnSi).]]

===Heusler structure===
{{main|Heusler compound}}
The Heusler structure, based on the structure of Cu<sub>2</sub>MnAl, is a common structure for [[ternary compound]]s involving [[transition metals]]. It has the space group Fm{{overline|3}}m (No. 225), and the [[Strukturbericht designation]] is L2<sub>1</sub>. Together with the closely related half-Heusler and inverse-Huesler compounds, there are hundreds of examples.

===Iron monosilicide structure===
{{Category see also|Iron monosilicide structure type}}
[[File:MnSi lattice.png|thumb|upright|Diagram of the [[iron monosilicide]] structure.]]

The space group of the iron monosilicide structure is P2<sub>1</sub>3 (No. 198), and the [[Strukturbericht designation]] is B20. This is a [[Chirality (mathematics)|chiral]] structure, and is sometimes associated with [[helimagnetic]] properties. There are four atoms of each element for a total of eight atoms in the unit cell.

Examples occur among the transition metal silicides and germanides, as well as a few other compounds such as [[gallium palladide]].

{| class="wikitable" style="text-align: center"
|+ Transition metal silicides and germanides with the FeSi structure
! scope="col" | 
! scope="col" | Silicides
! scope="col" | Germanides
|-
! scope="row" | Manganese
|[[Manganese monosilicide]]
|[[Manganese germanide]]
|-
! scope="row" | Iron
|[[Iron monosilicide]]
|[[Iron germanide]]
|-
! scope="row" | Cobalt
|[[Cobalt monosilicide]]
|[[Cobalt germanide]]
|-
! scope="row" | Chromium
|[[Chromium(IV) silicide]]
|[[Chromium(IV) germanide]]
|}

==Weaire–Phelan structure==
[[File:12-14-hedral_honeycomb.png|thumb|upright|Weaire–Phelan structure]]
A [[Weaire–Phelan structure]] has Pm{{overline|3}}n (223) symmetry.

It has three orientations of stacked [[tetradecahedron]]s with [[Dodecahedron#Pyritohedron|pyritohedral]] cells in the gaps. It is found as a [[crystal structure]] in [[chemistry]] where it is usually known as a "type I [[Clathrate compound|clathrate]] structure". [[Clathrate hydrate|Gas hydrates]] formed by methane, propane, and carbon dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are [[hydrogen bond]]ed together, and the larger gas molecules are trapped in the polyhedral cages.

==See also==
*[[Atomium]]: building which is a model of a ''bcc'' unit cell, with vertical body diagonal.
*[[Close-packing of equal spheres|Close-packing]]
*[[Dislocation]]s
*[[Reciprocal lattice]]

{{clear}}

==References==
{{reflist}}

==Further reading==
*Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., Wiley, {{isbn|0-471-80580-7}}

==External links==
*[[Jmol|JMol]] simulations by [[University of Graz|Graz University]]:
**[http://lampx.tugraz.at/~hadley/ss1/crystalstructure/structures/sc/sc_jsmol.php Simple cubic] 
**[http://lampx.tugraz.at/~hadley/ss1/crystalstructure/structures/bcc/bcc.php BCC] 
**[http://lampx.tugraz.at/~hadley/ss1/crystalstructure/structures/fcc/fcc_jsmol.php FCC] 
**[http://lampx.tugraz.at/~hadley/ss1/crystalstructure/structures/hcp/hcp.php HCP]
*[https://m.youtube.com/watch?v=ELIIynwpfes&feature=youtu.be Making crystal structure] with [[Jmol|Molview]]

{{Crystal systems}}

{{Authority control}}

{{DEFAULTSORT:Cubic Crystal System}}
[[Category:Crystal systems]]
[[Category:Cubes]]