Editing Epitaxy (section)

==Minerals==
[[File:Rutile-Hematite-171993.jpg|thumb|alt=text|Rutile epitaxial on hematite nearly 6 cm long. [[Bahia]], Brazil]]

In mineralogy, epitaxy is the overgrowth of one mineral on another in an orderly way, such that certain [[crystal structure#Planes and directions|crystal directions]] of the two minerals are aligned. This occurs when some planes in the [[crystal structure#Planes and directions|lattices]] of the overgrowth and the substrate have similar spacings between [[atoms]].<ref name="JR" />

If the crystals of both minerals are well formed so that the directions of the [[crystal structure#Planes and directions|crystallographic axes]] are clear then the epitaxic relationship can be deduced just by a visual inspection.<ref name="JR" />

Sometimes many separate crystals form the overgrowth on a single substrate, and then if there is epitaxy all the overgrowth crystals will have a similar orientation. The reverse, however, is not necessarily true. If the overgrowth crystals have a similar orientation there is probably an epitaxic relationship, but it is not certain.<ref name="JR">{{cite journal | last=Rakovan | first=John | title=Epitaxy | journal=Rocks & Minerals | publisher=Informa UK Limited | volume=81 | issue=4 | year=2006 | issn=0035-7529 | doi=10.3200/rmin.81.4.317-320 | pages=317–320| bibcode=2006RoMin..81..317R | s2cid=219714821 }}</ref>

Some authors<ref name="PR">{{cite journal | last1=White | first1=John S. | last2=Richards | first2=R. Peter | title=Let's Get It Right: Epitaxy—A Simple Concept? | journal=Rocks & Minerals | publisher=Informa UK Limited | volume=85 | issue=2 | date=2010-02-17 | issn=0035-7529 | doi=10.1080/00357521003591165 | pages=173–176| bibcode=2010RoMin..85..173W | s2cid=128758902 }}</ref> consider that overgrowths of a second generation of the same mineral species should also be considered as epitaxy, and this is common terminology for [[semiconductor]] scientists who induce epitaxic growth of a film with a different [[doping (semiconductor)|doping]] level on a semiconductor substrate of the same material. For naturally produced minerals, however, the [[International Mineralogical Association]] (IMA) definition requires that the two minerals be of different species.<ref name="AC">Acta Crystallographica Section A Crystal Physics, Diffraction, Theoretical and General Crystallography Volume 33, Part 4 (July 1977)</ref>

Another man-made application of epitaxy is the making of artificial snow using [[silver iodide]], which is possible because [[hexagonal crystal system|hexagonal]] silver iodide and ice have similar cell dimensions.<ref name="PR" />

===Isomorphic minerals===
Minerals that have the same structure ([[isomorphism (crystallography)|isomorphic minerals]]) may have epitaxic relations. An example is [[albite]] {{chem|NaAlSi|3|O|8}} on [[microcline]] {{chem|KAlSi|3|O|8}}. Both these minerals are [[triclinic crystal system|triclinic]], with [[space group]] {{overline|1}}, and with similar [[unit cell]] parameters, a = 8.16 Å, b = 12.87 Å, c = 7.11 Å, α = 93.45°, β = 116.4°, γ = 90.28° for albite and a = 8.5784 Å, b = 12.96 Å, c = 7.2112 Å, α = 90.3°, β = 116.05°, γ = 89° for microcline.

===Polymorphic minerals===
[[File:Rutile-Hematite-113489.jpg|thumb|alt=text|Rutile on hematite, from Novo Horizonte, Bahia, Northeast Region, Brazil]]
[[File:Hematite-Magnetite-180698.jpg|thumb|alt=text|Hematite [[pseudomorph]] after magnetite, with terraced epitaxial faces. [[La Rioja Province, Argentina|La Rioja]], Argentina]]
Minerals that have the same composition but different structures ([[polymorphism (materials science)|polymorphic minerals]]) may also have epitaxic relations. Examples are [[pyrite]] and [[marcasite]], both FeS<sub>2</sub>, and [[sphalerite]] and [[wurtzite]], both ZnS.<ref name="JR" />

===Rutile on hematite===
Some pairs of minerals that are not related structurally or compositionally may also exhibit epitaxy. A common example is [[rutile]] TiO<sub>2</sub> on [[hematite]] Fe<sub>2</sub>O<sub>3</sub>.<ref name="JR" /><ref name="MF">{{cite web|title=FMF - Friends of Minerals Forum, discussion and message board :: Index|url=http://www.mineral-forum.com/message-board/|website=www.mineral-forum.com/message-board/}}</ref> Rutile is [[tetragonal crystal system|tetragonal]] and hematite is [[trigonal crystal system|trigonal]], but there are directions of similar spacing between the atoms in the [[Miller index|(100)]] plane of rutile (perpendicular to the a [[crystal structure#Lattice systems|axis]]) and the [[Miller index|(001)]] plane of hematite (perpendicular to the c axis). In epitaxy these directions tend to line up with each other, resulting in the axis of the rutile overgrowth being parallel to the c axis of hematite, and the c axis of rutile being parallel to one of the axes of hematite.<ref name="JR" />

===Hematite on magnetite===
Another example is [[hematite]] {{chem|Fe|3+|2|O|3}} on [[magnetite]] {{chem|Fe|2+|Fe|3+|2|O|4}}. The magnetite structure is based on close-packed [[oxygen]] [[ion#Anions and cations|anions]] stacked in an ABC-ABC sequence. In this packing the close-packed layers are parallel to [[Miller index|(111)]] (a plane that symmetrically "cuts off" a corner of a cube). The hematite structure is based on close-packed oxygen anions stacked in an AB-AB sequence, which results in a crystal with hexagonal symmetry.<ref name="WN">Nesse, William (2000). Introduction to Mineralogy. Oxford University Press. Page 79</ref>

If the [[cations]] were small enough to fit into a truly close-packed structure of oxygen anions then the spacing between the nearest neighbour oxygen sites would be the same for both species. The radius of the oxygen ion, however, is only 1.36 Å<ref name="MOM">{{cite book|last1=Klein|first1=Cornelis|last2=Hurlbut|first2=Cornelius Searle|last3=Dana|first3=James Dwight|title=Manual of mineralogy|url={{google books |plainurl=y |id=8ybwAAAAMAAJ}}|year=1993|publisher=Wiley|isbn=978-0-471-57452-1}}</ref> and the Fe cations are big enough to cause some variations. The Fe radii vary from 0.49 Å to 0.92 Å,<ref name="IC">{{Cite web|url=http://abulafia.mt.ic.ac.uk/shannon/ptable.php|title=Shannon Radii|website=abulafia.mt.ic.ac.uk}}</ref> depending on the [[Ion#Denoting the charged state|charge]] (2+ or 3+) and the [[coordination number]] (4 or 8). Nevertheless, the O spacings are similar for the two minerals hence hematite can readily grow on the [[Miller index|(111)]] faces of magnetite, with hematite [[Miller index|(001)]] parallel to magnetite [[Miller index|(111)]].<ref name="WN" />