Editing Pyrite (section)

==Crystallography==
[[Image:FeS2structure.png|thumb|right|Crystal structure of pyrite. In the center of the cell a S<sub>2</sub><sup>2−</sup> pair is seen in yellow.]]

Iron-pyrite FeS<sub>2</sub> represents the prototype compound of the [[Crystallography|crystallographic]] pyrite structure. The structure is [[cubic crystal system|cubic]] and was among the first [[crystal structures]] solved by [[X-ray diffraction]].<ref name=Brag1913>{{cite journal|author=Bragg, W. L.|title=The structure of some crystals as indicated by their diffraction of X-rays|journal=[[Proceedings of the Royal Society A]]|volume=89|pages=248–277|year=1913|doi=10.1098/rspa.1913.0083|bibcode=1913RSPSA..89..248B|issue=610|jstor=93488|doi-access=free}}</ref> It belongs to the crystallographic [[space group]] ''Pa''{{overline|3}} and is denoted by the [[Zeitschrift für Kristallographie|Strukturbericht]] notation C2. Under thermodynamic standard conditions the [[lattice constant]] <math>a</math> of stoichiometric iron pyrite FeS<sub>2</sub> amounts to {{nowrap|541.87 pm}}.<ref name=Birk1991>{{cite journal|title=Sulfur deficiency in iron pyrite (FeS<sub>2−x</sub>) and its consequences for band structure models|journal=Physical Review B|volume=43|pages=11926–11936|year=1991|doi=10.1103/PhysRevB.43.11926|bibcode=1991PhRvB..4311926B|issue=14|last1=Birkholz|first1=M.|last2=Fiechter|first2=S.|last3=Hartmann|first3=A.|last4=Tributsch|first4=H.|pmid=9996968}}</ref> The [[cubic crystal system#Voids in the unit cell|unit cell]] is composed of a Fe [[Bravais lattice|face-centered cubic sublattice]] into which the {{chem|S|2}} ions are embedded. (Note though that the iron atoms in the faces are not equivalent by translation alone to the iron atoms at the corners.) The pyrite structure is also seen in other ''MX''<sub>2</sub> compounds of [[transition metals]] ''M'' and [[chalcogen]]s ''X'' = [[oxygen|O]], [[sulfur|S]], [[selenium|Se]] and [[tellurium|Te]]. Certain [[pnictide|dipnictides]] with ''X'' standing for [[phosphorus|P]], [[arsenic|As]] and [[antimony|Sb]] etc. are also known to adopt the pyrite structure.<ref name=Bres1994>{{cite journal|title=Bonding Trends in Pyrites and a Reinvestigation of the Structure of PdAs<sub>2</sub>, PdSb<sub>2</sub>, PtSb<sub>2</sub> and PtBi<sub>2</sub>|journal=Z. Anorg. Allg. Chem.|volume=620|issue=3|pages=393–404|year=1994|doi=10.1002/zaac.19946200302|last1=Brese|first1=Nathaniel E.|last2=von Schnering|first2=Hans Georg}}</ref>

The Fe atoms are bonded to six S atoms, giving a distorted octahedron. The material is a [[semiconductor]]. The Fe ions are usually considered to be ''[[low spin]]'' [[divalent]] state (as shown by [[Mössbauer spectroscopy]] as well as XPS). The material as a whole behaves as a Van Vleck [[Paramagnetism|paramagnet]], despite its low-spin divalency.<ref>{{Cite journal|last1=Burgardt|first1=P.|last2=Seehra|first2=M. S.|date=1977-04-01|title=Magnetic susceptibility of iron pyrite (FeS2) between 4.2 and 620 K|journal=Solid State Communications|volume=22|issue=2|pages=153–156|doi=10.1016/0038-1098(77)90422-7|bibcode=1977SSCom..22..153B|issn=0038-1098}}</ref>

The sulfur centers occur in pairs, described as S<sub>2</sub><sup>2−</sup>.<ref>{{cite journal|last1=Hulliger|first1=F.|title=Electrical Properties of Pyrite-Type and Related Compounds with Zero Spin Moment|journal=Nature|date=December 1963|volume=200|issue=4911|pages=1064–1065|doi=10.1038/2001064a0|bibcode=1963Natur.200.1064H|s2cid=32504249}}</ref><!-- Really need a more recent source--> Reduction of pyrite with potassium gives [[potassium dithioferrate]], KFeS<sub>2</sub>. This material features ferric ions and isolated sulfide (S<sup>2−</sup>) centers.

The S atoms are tetrahedral, being bonded to three Fe centers and one other S atom. The site symmetry at Fe and S positions is accounted for by [[crystallographic point group|point symmetry groups]] ''C''<sub>3''i''</sub> and ''C''<sub>3</sub>, respectively. The missing [[centrosymmetry|center of inversion]] at S lattice sites has important consequences for the crystallographic and physical properties of iron pyrite. These consequences derive from the crystal electric field active at the sulfur lattice site, which causes a [[Chemical polarity|polarization]] of S ions in the pyrite lattice.<ref name=BJPC1992>{{cite journal|author=Birkholz, M.|url=https://www.researchgate.net/publication/231101585|title=The crystal energy of pyrite|journal=J. Phys.: Condens. Matter|volume=4|pages=6227–6240|year=1992|doi=10.1088/0953-8984/4/29/007|bibcode=1992JPCM....4.6227B|issue=29|s2cid = 250815717 }}</ref> The polarisation can be calculated on the basis of higher-order [[Madelung constant]]s and has to be included in the calculation of the [[lattice energy]] by using a generalised [[Born–Haber cycle]]. This reflects the fact that the covalent bond in the sulfur pair is inadequately accounted for by a strictly ionic treatment.<ref>{{cite journal|last1=Wood|first1=Robert|title=Madelung Constants for the Calcium Carbide and Pyrite Crystal Structures|journal=The Journal of Chemical Physics|date=August 1962|volume=37|issue=3|pages=598–600|doi=10.1063/1.1701381|bibcode=1962JChPh..37..598W }}</ref>

Arsenopyrite has a related structure with heteroatomic As–S pairs rather than S-S pairs. Marcasite also possesses homoatomic anion pairs, but the arrangement of the metal and diatomic anions differs from that of pyrite. Despite its name, chalcopyrite ({{chem|CuFeS|2}}) does not contain dianion pairs, but single S<sup>2−</sup> sulfide anions.