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===Crystal structure=== Garnets are [[Silicate minerals#Nesosilicates or Isosilicates|nesosilicates]] having the general formula ''X''<sub>3</sub>''Y''<sub>2</sub>({{chem|[[silicon|Si]]|[[oxygen|O]]|4}})<sub>3</sub>. The ''X'' site is usually occupied by divalent cations ([[calcium|Ca]], [[magnesium|Mg]], [[iron|Fe]], [[manganese|Mn]])<sup>2+</sup> and the ''Y'' site by trivalent cations ([[aluminium|Al]]<sup>3+</sup>, Fe<sup>3+</sup>, [[chromium|Cr]]<sup>3+</sup>) in an [[octahedron|octahedral]]/[[tetrahedron|tetrahedral]] framework with [SiO<sub>4</sub>]<sup>4β</sup> occupying the tetrahedra.<ref>{{cite web | last = Smyth | first = Joe | title = Mineral Structure Data | work = Garnet | publisher = University of Colorado | url = http://ruby.colorado.edu/~smyth/min/garnet.html | access-date = 2007-01-12 | archive-date = 2007-01-16 | archive-url = https://web.archive.org/web/20070116233247/http://ruby.colorado.edu/~smyth/min/garnet.html | url-status = dead }}</ref> Garnets are most often found in the [[dodecahedral]] [[crystal habit]], but are also commonly found in the [[trapezohedron]] habit as well as the [[Hexoctahedron|hexoctahedral]] habit.<ref name="Klein-1993" /> They crystallize in the [[Cubic (crystal system)|cubic]] system, having three axes that are all of equal length and perpendicular to one another but are never actually cubic because, despite being isometric, the {100} and {111} families of planes are depleted.<ref name="Klein-1993" /> Garnets do not have any [[Cleavage (crystal)|cleavage]] planes, so, when they fracture under stress, sharp, irregular ([[conchoidal]]) pieces are formed.<ref>{{cite book |last1=Nesse |first1=William D. |title=Introduction to mineralogy |date=2000 |publisher=Oxford University Press |location=New York |isbn=9780195106916 |page=311}}</ref> <gallery> File:Pyrope cp.jpg|Crystal structure of pyrope garnet. White spheres are oxygen; black, silicon; blue, aluminium; and red, magnesium. File:Pyrope crystal structure.jpg|Same view, with ion sizes reduced to better show all ions File:Pyrope si.jpg|Silicon ion size exaggerated to emphasize silica tetrahedra </gallery>
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