Crystal - Wikipedia

A crystal or crystalline solid is a solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that ... Crystal FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Solidmaterialwithhighlyorderedmicroscopicstructure "Crystalline"redirectshere.FortheBjörksong,seeCrystalline(song). "Xtal"redirectshere.Forotheruses,seeXtal(disambiguation). Thisarticleisaboutcrystallinesolids.Forotheruses,seeCrystal(disambiguation). Thisarticleneedsadditionalcitationsforverification.Pleasehelpimprovethisarticlebyaddingcitationstoreliablesources.Unsourcedmaterialmaybechallengedandremoved.Findsources: "Crystal" – news ·newspapers ·books ·scholar ·JSTOR(September2016)(Learnhowandwhentoremovethistemplatemessage) Crystalsofamethystquartz Microscopically,asinglecrystalhasatomsinanear-perfectperiodicarrangement;apolycrystaliscomposedofmanymicroscopiccrystals(called"crystallites"or"grains");andanamorphoussolid(suchasglass)hasnoperiodicarrangementevenmicroscopically. Acrystalorcrystallinesolidisasolidmaterialwhoseconstituents(suchasatoms,molecules,orions)arearrangedinahighlyorderedmicroscopicstructure,formingacrystallatticethatextendsinalldirections.[1][2]Inaddition,macroscopicsinglecrystalsareusuallyidentifiablebytheirgeometricalshape,consistingofflatfaceswithspecific,characteristicorientations.Thescientificstudyofcrystalsandcrystalformationisknownascrystallography.Theprocessofcrystalformationviamechanismsofcrystalgrowthiscalledcrystallizationorsolidification. ThewordcrystalderivesfromtheAncientGreekwordκρύσταλλος(krustallos),meaningboth"ice"and"rockcrystal",[3]fromκρύος(kruos),"icycold,frost".[4][5] Examplesoflargecrystalsincludesnowflakes,diamonds,andtablesalt.Mostinorganicsolidsarenotcrystalsbutpolycrystals,i.e.manymicroscopiccrystalsfusedtogetherintoasinglesolid.Examplesofpolycrystalsincludemostmetals,rocks,ceramics,andice.Athirdcategoryofsolidsisamorphoussolids,wheretheatomshavenoperiodicstructurewhatsoever.Examplesofamorphoussolidsincludeglass,wax,andmanyplastics. Despitethename,leadcrystal,crystalglass,andrelatedproductsarenotcrystals,butrathertypesofglass,i.e.amorphoussolids. Crystalsareoftenusedinpseudoscientificpracticessuchascrystaltherapy,and,alongwithgemstones,aresometimesassociatedwithspellworkinWiccanbeliefsandrelatedreligiousmovements.[6][7][8] Contents 1Crystalstructure(microscopic) 2Crystalfacesandshapes 3Occurrenceinnature 3.1Rocks 3.2Ice 3.3Organigeniccrystals 4Polymorphismandallotropy 5Crystallization 6Defects,impurities,andtwinning 7Chemicalbonds 8Quasicrystals 9Specialpropertiesfromanisotropy 10Crystallography 11Imagegallery 12Seealso 13References 14Furtherreading Crystalstructure(microscopic) Halite(tablesalt,NaCl):MicroscopicandmacroscopicMicroscopicstructureofahalitecrystal.(Purpleissodiumion,greenischlorineion).Thereiscubicsymmetryintheatoms'arrangementMacroscopic(~16cm)halitecrystal.Theright-anglesbetweencrystalfacesareduetothecubicsymmetryoftheatoms'arrangement Mainarticle:Crystalstructure Thescientificdefinitionofa"crystal"isbasedonthemicroscopicarrangementofatomsinsideit,calledthecrystalstructure.Acrystalisasolidwheretheatomsformaperiodicarrangement.(Quasicrystalsareanexception,seebelow). Notallsolidsarecrystals.Forexample,whenliquidwaterstartsfreezing,thephasechangebeginswithsmallicecrystalsthatgrowuntiltheyfuse,formingapolycrystallinestructure.Inthefinalblockofice,eachofthesmallcrystals(called"crystallites"or"grains")isatruecrystalwithaperiodicarrangementofatoms,butthewholepolycrystaldoesnothaveaperiodicarrangementofatoms,becausetheperiodicpatternisbrokenatthegrainboundaries.Mostmacroscopicinorganicsolidsarepolycrystalline,includingalmostallmetals,ceramics,ice,rocks,etc.Solidsthatareneithercrystallinenorpolycrystalline,suchasglass,arecalledamorphoussolids,alsocalledglassy,vitreous,ornoncrystalline.Thesehavenoperiodicorder,evenmicroscopically.Therearedistinctdifferencesbetweencrystallinesolidsandamorphoussolids:mostnotably,theprocessofformingaglassdoesnotreleasethelatentheatoffusion,butformingacrystaldoes. Acrystalstructure(anarrangementofatomsinacrystal)ischaracterizedbyitsunitcell,asmallimaginaryboxcontainingoneormoreatomsinaspecificspatialarrangement.Theunitcellsarestackedinthree-dimensionalspacetoformthecrystal. Thesymmetryofacrystalisconstrainedbytherequirementthattheunitcellsstackperfectlywithnogaps.Thereare219possiblecrystalsymmetries(230iscommonlycited,butthistreatschiralequivalentsasseparateentities),calledcrystallographicspacegroups.[9]Thesearegroupedinto7crystalsystems,suchascubiccrystalsystem(wherethecrystalsmayformcubesorrectangularboxes,suchashaliteshownatright)orhexagonalcrystalsystem(wherethecrystalsmayformhexagons,suchasordinarywaterice). Crystalfacesandshapes Asahalitecrystalisgrowing,newatomscanveryeasilyattachtothepartsofthesurfacewithroughatomic-scalestructureandmanydanglingbonds.Therefore,thesepartsofthecrystalgrowoutveryquickly(yellowarrows).Eventually,thewholesurfaceconsistsofsmooth,stablefaces,wherenewatomscannotaseasilyattachthemselves. Crystalsarecommonlyrecognizedbytheirshape,consistingofflatfaceswithsharpangles.Theseshapecharacteristicsarenotnecessaryforacrystal—acrystalisscientificallydefinedbyitsmicroscopicatomicarrangement,notitsmacroscopicshape—butthecharacteristicmacroscopicshapeisoftenpresentandeasytosee. Euhedralcrystalsarethosewithobvious,well-formedflatfaces.Anhedralcrystalsdonot,usuallybecausethecrystalisonegraininapolycrystallinesolid. Theflatfaces(alsocalledfacets)ofaeuhedralcrystalareorientedinaspecificwayrelativetotheunderlyingatomicarrangementofthecrystal:theyareplanesofrelativelylowMillerindex.[10]Thisoccursbecausesomesurfaceorientationsaremorestablethanothers(lowersurfaceenergy).Asacrystalgrows,newatomsattacheasilytotherougherandlessstablepartsofthesurface,butlesseasilytotheflat,stablesurfaces.Therefore,theflatsurfacestendtogrowlargerandsmoother,untilthewholecrystalsurfaceconsistsoftheseplanesurfaces.(Seediagramonright.) Oneoftheoldesttechniquesinthescienceofcrystallographyconsistsofmeasuringthethree-dimensionalorientationsofthefacesofacrystal,andusingthemtoinfertheunderlyingcrystalsymmetry. Acrystal'scrystallographicformsaresetsofpossiblefacesofthecrystalthatarerelatedbyoneofthesymmetriesofthecrystal.Forexample,crystalsofgalenaoftentaketheshapeofcubes,andthesixfacesofthecubebelongtoacrystallographicformthatdisplaysoneofthesymmetriesoftheisometriccrystalsystem.Galenaalsosometimescrystallizesasoctahedrons,andtheeightfacesoftheoctahedronbelongtoanothercrystallographicformreflectingadifferentsymmetryoftheisometricsystem.AcrystallographicformisdescribedbyplacingtheMillerindicesofoneofitsfaceswithinbrackets.Forexample,theoctahedralformiswrittenas{111},andtheotherfacesintheformareimpliedbythesymmetryofthecrystal. Formsmaybeclosed,meaningthattheformcancompletelyencloseavolumeofspace,oropen,meaningthatitcannot.Thecubicandoctahedralformsareexamplesofclosedforms.Alltheformsoftheisometricsystemareclosed,whilealltheformsofthemonoclinicandtricliniccrystalsystemsareopen.Acrystal'sfacesmayallbelongtothesameclosedform,ortheymaybeacombinationofmultipleopenorclosedforms.[11] Acrystal'shabitisitsvisibleexternalshape.Thisisdeterminedbythecrystalstructure(whichrestrictsthepossiblefacetorientations),thespecificcrystalchemistryandbonding(whichmayfavorsomefacettypesoverothers),andtheconditionsunderwhichthecrystalformed. Occurrenceinnature Icecrystals Fossilshellwithcalcitecrystals Rocks Byvolumeandweight,thelargestconcentrationsofcrystalsintheEartharepartofitssolidbedrock.Crystalsfoundinrockstypicallyrangeinsizefromafractionofamillimetretoseveralcentimetresacross,althoughexceptionallylargecrystalsareoccasionallyfound.Asof1999[update],theworld'slargestknownnaturallyoccurringcrystalisacrystalofberylfromMalakialina,Madagascar,18 m(59 ft)longand3.5 m(11 ft)indiameter,andweighing380,000 kg(840,000 lb).[12] Somecrystalshaveformedbymagmaticandmetamorphicprocesses,givingorigintolargemassesofcrystallinerock.Thevastmajorityofigneousrocksareformedfrommoltenmagmaandthedegreeofcrystallizationdependsprimarilyontheconditionsunderwhichtheysolidified.Suchrocksasgranite,whichhavecooledveryslowlyandundergreatpressures,havecompletelycrystallized;butmanykindsoflavawerepouredoutatthesurfaceandcooledveryrapidly,andinthislattergroupasmallamountofamorphousorglassymatteriscommon.Othercrystallinerocks,themetamorphicrockssuchasmarbles,mica-schistsandquartzites,arerecrystallized.Thismeansthattheywereatfirstfragmentalrockslikelimestone,shaleandsandstoneandhaveneverbeeninamoltenconditionnorentirelyinsolution,butthehightemperatureandpressureconditionsofmetamorphismhaveactedonthembyerasingtheiroriginalstructuresandinducingrecrystallizationinthesolidstate.[13] Otherrockcrystalshaveformedoutofprecipitationfromfluids,commonlywater,toformdrusesorquartzveins.Evaporitessuchashalite,gypsumandsomelimestoneshavebeendepositedfromaqueoussolution,mostlyowingtoevaporationinaridclimates. Ice Water-basediceintheformofsnow,seaice,andglaciersarecommoncrystalline/polycrystallinestructuresonEarthandotherplanets.[14]Asinglesnowflakeisasinglecrystaloracollectionofcrystals,[15]whileanicecubeisapolycrystal.[16] Organigeniccrystals Manylivingorganismsareabletoproducecrystals,forexamplecalciteandaragoniteinthecaseofmostmolluscsorhydroxylapatiteinthecaseofvertebrates. Polymorphismandallotropy Mainarticles:Polymorphism(materialsscience)andAllotropy Thesamegroupofatomscanoftensolidifyinmanydifferentways.Polymorphismistheabilityofasolidtoexistinmorethanonecrystalform.Forexample,watericeisordinarilyfoundinthehexagonalformIceIh,butcanalsoexistasthecubicIceIc,therhombohedraliceII,andmanyotherforms.Thedifferentpolymorphsareusuallycalleddifferentphases. Inaddition,thesameatomsmaybeabletoformnoncrystallinephases.Forexample,watercanalsoformamorphousice,whileSiO2canformbothfusedsilica(anamorphousglass)andquartz(acrystal).Likewise,ifasubstancecanformcrystals,itcanalsoformpolycrystals. Forpurechemicalelements,polymorphismisknownasallotropy.Forexample,diamondandgraphitearetwocrystallineformsofcarbon,whileamorphouscarbonisanoncrystallineform.Polymorphs,despitehavingthesameatoms,mayhavewildlydifferentproperties.Forexample,diamondisamongthehardestsubstancesknown,whilegraphiteissosoftthatitisusedasalubricant. Polyamorphismisasimilarphenomenonwherethesameatomscanexistinmorethanoneamorphoussolidform. Crystallization Mainarticles:CrystallizationandCrystalgrowth Verticalcoolingcrystallizerinabeetsugarfactory. Crystallizationistheprocessofformingacrystallinestructurefromafluidorfrommaterialsdissolvedinafluid.(Morerarely,crystalsmaybedepositeddirectlyfromgas;seethin-filmdepositionandepitaxy.) Crystallizationisacomplexandextensively-studiedfield,becausedependingontheconditions,asinglefluidcansolidifyintomanydifferentpossibleforms.Itcanformasinglecrystal,perhapswithvariouspossiblephases,stoichiometries,impurities,defects,andhabits.Or,itcanformapolycrystal,withvariouspossibilitiesforthesize,arrangement,orientation,andphaseofitsgrains.Thefinalformofthesolidisdeterminedbytheconditionsunderwhichthefluidisbeingsolidified,suchasthechemistryofthefluid,theambientpressure,thetemperature,andthespeedwithwhichalltheseparametersarechanging. Specificindustrialtechniquestoproducelargesinglecrystals(calledboules)includetheCzochralskiprocessandtheBridgmantechnique.Otherlessexoticmethodsofcrystallizationmaybeused,dependingonthephysicalpropertiesofthesubstance,includinghydrothermalsynthesis,sublimation,orsimplysolvent-basedcrystallization. Largesinglecrystalscanbecreatedbygeologicalprocesses.Forexample,selenitecrystalsinexcessof10 marefoundintheCaveoftheCrystalsinNaica,Mexico.[17]Formoredetailsongeologicalcrystalformation,seeabove. Crystalscanalsobeformedbybiologicalprocesses,seeabove.Conversely,someorganismshavespecialtechniquestopreventcrystallizationfromoccurring,suchasantifreezeproteins. Defects,impurities,andtwinning Mainarticles:Crystallographicdefect,Impurity,Crystaltwinning,andMosaicity Twotypesofcrystallographicdefects.Topright:edgedislocation.Bottomright:screwdislocation. Anidealcrystalhaseveryatominaperfect,exactlyrepeatingpattern.[18]However,inreality,mostcrystallinematerialshaveavarietyofcrystallographicdefects,placeswherethecrystal'spatternisinterrupted.Thetypesandstructuresofthesedefectsmayhaveaprofoundeffectonthepropertiesofthematerials. Afewexamplesofcrystallographicdefectsincludevacancydefects(anemptyspacewhereanatomshouldfit),interstitialdefects(anextraatomsqueezedinwhereitdoesnotfit),anddislocations(seefigureatright).Dislocationsareespeciallyimportantinmaterialsscience,becausetheyhelpdeterminethemechanicalstrengthofmaterials. Anothercommontypeofcrystallographicdefectisanimpurity,meaningthatthe"wrong"typeofatomispresentinacrystal.Forexample,aperfectcrystalofdiamondwouldonlycontaincarbonatoms,butarealcrystalmightperhapscontainafewboronatomsaswell.Theseboronimpuritieschangethediamond'scolortoslightlyblue.Likewise,theonlydifferencebetweenrubyandsapphireisthetypeofimpuritiespresentinacorundumcrystal. Twinnedpyritecrystalgroup. Insemiconductors,aspecialtypeofimpurity,calledadopant,drasticallychangesthecrystal'selectricalproperties.Semiconductordevices,suchastransistors,aremadepossiblelargelybyputtingdifferentsemiconductordopantsintodifferentplaces,inspecificpatterns. Twinningisaphenomenonsomewherebetweenacrystallographicdefectandagrainboundary.Likeagrainboundary,atwinboundaryhasdifferentcrystalorientationsonitstwosides.Butunlikeagrainboundary,theorientationsarenotrandom,butrelatedinaspecific,mirror-imageway. Mosaicityisaspreadofcrystalplaneorientations.Amosaiccrystalconsistsofsmallercrystallineunitsthataresomewhatmisalignedwithrespecttoeachother. Chemicalbonds Ingeneral,solidscanbeheldtogetherbyvarioustypesofchemicalbonds,suchasmetallicbonds,ionicbonds,covalentbonds,vanderWaalsbonds,andothers.Noneofthesearenecessarilycrystallineornon-crystalline.However,therearesomegeneraltrendsasfollows. Metalsarealmostalwayspolycrystalline,thoughthereareexceptionslikeamorphousmetalandsingle-crystalmetals.Thelatteraregrownsynthetically.(Amicroscopically-smallpieceofmetalmaynaturallyformintoasinglecrystal,butlargerpiecesgenerallydonot.)Ioniccompoundmaterialsareusuallycrystallineorpolycrystalline.Inpractice,largesaltcrystalscanbecreatedbysolidificationofamoltenfluid,orbycrystallizationoutofasolution.Covalentlybondedsolids(sometimescalledcovalentnetworksolids)arealsoverycommon,notableexamplesbeingdiamondandquartz.WeakvanderWaalsforcesalsohelpholdtogethercertaincrystals,suchascrystallinemolecularsolids,aswellastheinterlayerbondingingraphite.Polymermaterialsgenerallywillformcrystallineregions,butthelengthsofthemoleculesusuallypreventcompletecrystallization—andsometimespolymersarecompletelyamorphous. Quasicrystals Thematerialholmium–magnesium–zinc(Ho–Mg–Zn)formsquasicrystals,whichcantakeonthemacroscopicshapeofapentagonaldodecahedron.Onlyquasicrystalscantakethis5-foldsymmetry.Theedgesare2 mmlong. Mainarticle:Quasicrystal Aquasicrystalconsistsofarraysofatomsthatareorderedbutnotstrictlyperiodic.Theyhavemanyattributesincommonwithordinarycrystals,suchasdisplayingadiscretepatterninx-raydiffraction,andtheabilitytoformshapeswithsmooth,flatfaces. Quasicrystalsaremostfamousfortheirabilitytoshowfive-foldsymmetry,whichisimpossibleforanordinaryperiodiccrystal(seecrystallographicrestrictiontheorem). TheInternationalUnionofCrystallographyhasredefinedtheterm"crystal"toincludebothordinaryperiodiccrystalsandquasicrystals("anysolidhavinganessentiallydiscretediffractiondiagram"[19]). Quasicrystals,firstdiscoveredin1982,arequiterareinpractice.Onlyabout100solidsareknowntoformquasicrystals,comparedtoabout400,000periodiccrystalsknownin2004.[20]The2011NobelPrizeinChemistrywasawardedtoDanShechtmanforthediscoveryofquasicrystals.[21] Specialpropertiesfromanisotropy Seealso:Crystaloptics Crystalscanhavecertainspecialelectrical,optical,andmechanicalpropertiesthatglassandpolycrystalsnormallycannot.Thesepropertiesarerelatedtotheanisotropyofthecrystal,i.e.thelackofrotationalsymmetryinitsatomicarrangement.Onesuchpropertyisthepiezoelectriceffect,whereavoltageacrossthecrystalcanshrinkorstretchit.Anotherisbirefringence,whereadoubleimageappearswhenlookingthroughacrystal.Moreover,variouspropertiesofacrystal,includingelectricalconductivity,electricalpermittivity,andYoung'smodulus,maybedifferentindifferentdirectionsinacrystal.Forexample,graphitecrystalsconsistofastackofsheets,andalthougheachindividualsheetismechanicallyverystrong,thesheetsareratherlooselyboundtoeachother.Therefore,themechanicalstrengthofthematerialisquitedifferentdependingonthedirectionofstress. Notallcrystalshavealloftheseproperties.Conversely,thesepropertiesarenotquiteexclusivetocrystals.Theycanappearinglassesorpolycrystalsthathavebeenmadeanisotropicbyworkingorstress—forexample,stress-inducedbirefringence. Crystallography Mainarticle:Crystallography Crystallographyisthescienceofmeasuringthecrystalstructure(inotherwords,theatomicarrangement)ofacrystal.OnewidelyusedcrystallographytechniqueisX-raydiffraction.Largenumbersofknowncrystalstructuresarestoredincrystallographicdatabases. Imagegallery Insulincrystalsgrowninearthorbit. Hoarfrost:Atypeoficecrystal(picturetakenfromadistanceofabout5 cm). Gallium,ametalthateasilyformslargecrystals. Anapatitecrystalsitsfrontandcenteroncherry-redrhodochroiterhombs,purplefluoritecubes,quartzandadustingofbrass-yellowpyritecubes. Boulesofsilicon,likethisone,areanimportanttypeofindustrially-producedsinglecrystal. Aspecimenconsistingofabornite-coatedchalcopyritecrystalnestledinabedofclearquartzcrystalsandlustrouspyritecrystals.Thebornite-coatedcrystalisupto1.5 cmacross. Needle-likemilleritecrystalspartiallyencasedincalcitecrystalandoxidizedontheirsurfacestozaratite;fromtheDevonianMilwaukeeFormationofWisconsin Seealso Atomicpackingfactor Anticrystal Cocrystal Colloidalcrystal Crystalgrowth Crystaloscillator Liquidcrystal Timecrystal References ^StephenLower."Chem1onlinetextbook—Statesofmatter".Retrieved2016-09-19. ^AshcroftandMermin(1976).Solidstatephysics.{{citebook}}:CS1maint:usesauthorsparameter(link) ^κρύσταλλος,HenryGeorgeLiddell,RobertScott,AGreek-EnglishLexicon,onPerseusDigitalLibrary ^κρύος,HenryGeorgeLiddell,RobertScott,AGreek-EnglishLexicon,onPerseusDigitalLibrary ^ "TheAmericanHeritageDictionaryoftheEnglishLanguage".Kreus.2000.{{citejournal}}:Citejournalrequires|journal=(help)CS1maint:others(link) ^Regal,Brian.(2009).Pseudoscience:ACriticalEncyclopedia.Greenwood.p.51.ISBN 978-0-313-35507-3 ^PattiWigington(31August2016)."UsingCrystalsandGemstonesinMagic".About.com.Retrieved14November2016. ^"TheMagicofCrystalsandGemstones".WitchesLore.14December2011.Retrieved14November2016. ^InternationalTablesforCrystallography,vol. A,Chester,England:InternationalUnionofCrystallography,2016 ^Thesurfacescienceofmetaloxides,byVictorE.Henrich,P.A.Cox,page28,googlebookslink ^Sinkankas,John(1964).Mineralogyforamateurs.Princeton,N.J.:VanNostrand.pp. 134–138.ISBN 0442276249. ^G.CresseyandI.F.Mercer,(1999)Crystals,London,NaturalHistoryMuseum,page58 ^ Oneormoreoftheprecedingsentences incorporatestextfromapublicationnowinthepublicdomain: Flett,JohnSmith(1911)."Petrology".InChisholm,Hugh(ed.).EncyclopædiaBritannica.Vol. 21(11th ed.).CambridgeUniversityPress. ^YoshinoriFurukawa,"Ice";MattiLeppäranta,"SeaIce";D.P.Dobhal,"Glacier";andotherarticlesinVijayP.Singh,PratapSingh,andUmeshK.Haritashya,eds.,EncyclopediaofSnow,IceandGlaciers(Dordrecht,NE:SpringerScience&BusinessMedia,2011).ISBN 904812641X,9789048126415 ^Libbrecht,Kenneth;Wing,Rachel(2015-09-01).TheSnowflake:Winter'sFrozenArtistry.VoyageurPress.ISBN 9781627887335. ^Hjorth-Hansen,E.(2017-10-19).SnowEngineering2000:RecentAdvancesandDevelopments.Routledge.ISBN 9781351416238. ^"CaveofCrystalGiants—NationalGeographicMagazine".nationalgeographic.com. ^Britain),ScienceResearchCouncil(Great(1972).ReportoftheCouncil.H.M.StationeryOffice. ^InternationalUnionofCrystallography(1992)."ReportoftheExecutiveCommitteefor1991".ActaCrystallogr.A.48(6):922–946.doi:10.1107/S0108767392008328.PMC 1826680. ^SteurerW.(2004)."Twentyyearsofstructureresearchonquasicrystals.PartI.Pentagonal,octagonal,decagonalanddodecagonalquasicrystals".Z.Kristallogr.219(7–2004):391–446.Bibcode:2004ZK....219..391S.doi:10.1524/zkri.219.7.391.35643. ^"TheNobelPrizeinChemistry2011".Nobelprize.org.Retrieved2011-12-29. Furtherreading CrystalatWikipedia'ssisterprojectsDefinitionsfromWiktionaryMediafromCommonsNewsfromWikinewsQuotationsfromWikiquoteTextsfromWikisourceTextbooksfromWikibooksResourcesfromWikiversity Howard,J.Michael;DarcyHoward(Illustrator)(1998)."IntroductiontoCrystallographyandMineralCrystalSystems".Bob'sRockShop.Archivedfromtheoriginalon2006-08-26.Retrieved2008-04-20. Krassmann,Thomas(2005–2008)."TheGiantCrystalProject".Krassmann.Archivedfromtheoriginalon2008-04-26.Retrieved2008-04-20. "TeachingPamphlets".CommissiononCrystallographicTeaching.2007.Archivedfromtheoriginalon2008-04-17.Retrieved2008-04-20. "CrystalLatticeStructures:IndexbySpaceGroup".2004.Retrieved2016-12-03. "Crystallography".SpanishNationalResearchCouncil,DepartmentofCrystallography.2010.Retrieved2010-01-08. vtePatternsinnaturePatterns Crack Dune Foam Meander Phyllotaxis Soapbubble Symmetry incrystals Quasicrystals inflowers inbiology Tessellation Vortexstreet Wave Widmanstättenpattern Causes Patternformation Biology Naturalselection Camouflage Mimicry Sexualselection Mathematics Chaostheory Fractal Logarithmicspiral Physics Crystal Fluiddynamics Plateau'slaws Self-organization People Plato Pythagoras Empedocles Fibonacci LiberAbaci AdolfZeising ErnstHaeckel JosephPlateau WilsonBentley D'ArcyWentworthThompson OnGrowthandForm AlanTuring TheChemicalBasisofMorphogenesis AristidLindenmayer BenoîtMandelbrot HowLongIstheCoastofBritain?StatisticalSelf-SimilarityandFractionalDimension Related Patternrecognition Emergence Mathematicsandart AuthoritycontrolNationallibraries Spain France(data) Germany Israel UnitedStates Japan CzechRepublic Other FacetedApplicationofSubjectTerminology Retrievedfrom"https://en.wikipedia.org/w/index.php?title=Crystal&oldid=1084118629" Categories:CrystalsHiddencategories:CS1maint:usesauthorsparameterCS1errors:missingperiodicalCS1maint:othersWikipediaarticlesincorporatingacitationfromthe1911EncyclopaediaBritannicawithWikisourcereferenceWikipediaarticlesincorporatingtextfromthe1911EncyclopædiaBritannicaArticleswithshortdescriptionShortdescriptionisdifferentfromWikidataWikipediaindefinitelysemi-protectedpagesArticlesneedingadditionalreferencesfromSeptember2016AllarticlesneedingadditionalreferencesArticlescontainingAncientGreek(to1453)-languagetextArticlescontainingpotentiallydatedstatementsfrom1999AllarticlescontainingpotentiallydatedstatementsPagesusingdivcolwithsmallparameterPagesusingSisterprojectlinkswithdefaultsearchArticleswithBNEidentifiersArticleswithBNFidentifiersArticleswithGNDidentifiersArticleswithJ9UidentifiersArticleswithLCCNidentifiersArticleswithNDLidentifiersArticleswithNKCidentifiersArticleswithFASTidentifiers Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk English Views ReadViewsourceViewhistory More Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Inotherprojects WikimediaCommonsWikiquote Languages AfrikaansالعربيةAragonésԱրեւմտահայերէնArmãneashtiAsturianuAzərbaycancaবাংলাBân-lâm-gúБеларускаяБеларуская(тарашкевіца)БългарскиBoarischBosanskiCatalàČeštinaCymraegDanskDeutschEestiΕλληνικάEspañolEsperantoEuskaraفارسیFrançaisGaeilgeGalegoગુજરાતી한국어Հայերենहिन्दीHrvatskiIdoBahasaIndonesiaÍslenskaItalianoעבריתJawaಕನ್ನಡქართულიҚазақшаKiswahiliKreyòlayisyenKriyòlgwiyannenКыргызчаLatinaLatviešuLietuviųMagyarМакедонскиMalagasyമലയാളംमराठीBahasaMelayuꯃꯤꯇꯩꯂꯣꯟမြန်မာဘာသာNāhuatlNaVosaVakavitiNederlands日本語NorskbokmålNorsknynorskOccitanOʻzbekcha/ўзбекчаਪੰਜਾਬੀPatoisPiemontèisPolskiPortuguêsRomânăRunaSimiРусскийСахатылаScotsSimpleEnglishSlovenčinaSlovenščinaСрпски/srpskiSrpskohrvatski/српскохрватскиSuomiSvenskaTagalogதமிழ்Татарча/tatarçaไทยTürkçeУкраїнськаاردوئۇيغۇرچە/UyghurcheTiếngViệt文言Winaray吴语ייִדיש粵語中文 Editlinks