教学课件PPT金属和陶瓷的结构.ppt

chapter3 structuresofmetalsandceramics whystudystructuresofmetalsandceramics thepropertiesofsomematerialsaredirectlyrelatedtotheircrystalstructures forexample pureandundeformedmagnesiumandberyllium havingonecrystalstructure aremuchmorebrittle i e fractureatlowerdegreesofdeformation thanarepureandundeformedmetalssuchasgoldandsilverthathaveyetanothercrystalstructure seesection8 5 furthermore significantpropertydifferencesexistbetweencrystallineandnoncrystallinematerialshavingthesamecomposition forexample noncrystallineceramicsandpolymersnormallyareopticallytransparent thesamematerialsincrystalline orsemicrystalline formtendtobeopaqueor atbest translucent 同素异型晶系晶格参数无定形的晶体密勒指数阴离子衍射非晶体各向异性面心立方八面体位置致密度颗粒多晶体体心立方晶粒界类质异象布拉格定律密排六方单晶体阳离子各向同性四面体位置配位数晶格单位晶胞晶体结构 learningobjectivesafterstudyingthischapteryoushouldbeabletodothefollowing 1 describethedifferenceinatomic molecularstructurebetweencrystallineandnoncrystallinematerials 2 drawunitcellsforface centeredcubic body centeredcubic andhexagonalclose packedcrystalstructures 3 derivetherelationshipsbetweenunitcelledgelengthandatomicradiusforface centeredcubicandbody centeredcubiccrystalstructures 4 computethedensitiesformetalshavingface centeredcubicandbody centeredcubiccrystalstructuresgiventheirunitcelldimensions 5 sketch describeunitcellsforsodiumchloride cesiumchloride zincblende diamondcubic fluorite andperovskitecrystalstructures dolikewisefortheatomicstructuresofgraphiteandasilicaglass6 giventhechemicalformulaforaceramiccompound theionicradiiofitscomponentions determinethecrystalstructure 7 giventhreedirectionindexintegers sketchthedirectioncorrespondingtotheseindiceswithinaunitcell 8 specifythemillerindicesforaplanethathasbeendrawnwithinaunitcell 9 describehowface centeredcubicandhexagonalclose packedcrystalstructuresmaybegeneratedbythestackingofclose packedplanesofatoms dothesameforthesodiumchloridecrystalstructureintermsofclose packedplanesofanions 10 distinguishbetweensinglecrystalsandpolycrystallinematerials 11 defineisotropyandanisotropywithrespecttomaterialproperties 3 1introduction chapter2wasconcernedprimarilywiththevarioustypesofatomicbonding whicharedeterminedbytheelectronstructureoftheindividualatoms thepresentdiscussionisdevotedtothenextlevelofthestructureofmaterials specifically tosomeofthearrangementsthatmaybeassumedbyatomsinthesolidstate withinthisframework 结构 conceptsofcrystallinityandnoncrystallinityareintroduced forcrystallinesolidsthenotion 概念 ofcrystalstructureispresented specifiedintermsofaunitcell crystalstructuresfoundinbothmetalsandceramicsarethendetailed alongwiththescheme 构型 bywhichcrystallographic 晶体学的 directionsandplanesareexpressed singlecrystals polycrystalline andnoncrystallinematerialsareconsidered crystalstructures3 2fundamentalconcepts solidmaterialsmaybeclassifiedaccordingtotheregularitywithwhichatomsorionsarearrangedwithrespecttooneanother acrystallinematerialisoneinwhichtheatomsaresituatedinarepeatingorperiodicarrayoverlargeatomicdistances thatis long rangeorderexists suchthatuponsolidification 固化 theatomswillpositionthemselvesinarepetitivethree dimensionalpattern 构图 inwhicheachatomisbondedtoitsnearest neighboratoms allmetals manyceramicmaterials andcertainpolymersformcrystallinestructuresundernormalsolidificationconditions forthosethatdonotcrystallize thislong rangeatomicorderisabsent thesenoncrystallineoramorphousmaterialsarediscussedbrieflyattheendofthischapter someofthepropertiesofcrystallinesolidsdependonthecrystalstructureofthematerial themannerinwhichatoms ions ormoleculesarespatiallyarranged 空间排列 thereisanextremelylargenumberofdifferentcrystalstructuresallhavinglong rangeatomicorder thesevaryfromrelativelysimplestructuresformetals toexceedinglycomplexones asdisplayedbysomeoftheceramicandpolymericmaterials thepresentdiscussiondealswithseveralcommonmetallicandceramiccrystalstructures thenextchapterisdevotedtostructuresforpolymers whendescribingcrystallinestructures atoms orions arethoughtofasbeingsolidsphereshavingwell defineddiameters thisistermedtheatomichardspheremodelinwhichspheresrepresentingnearest neighboratomstouchoneanother anexampleofthehardspheremodelfortheatomicarrangementfoundinsomeofthecommonelementalmetalsisdisplayed 显示 infigure3 1c inthisparticularcasealltheatomsareidentical sometimesthetermlatticeisusedinthecontext 课文 ofcrystalstructures inthissense lattice meansathree dimensionalarrayofpointscoinciding 相同 withatompositions orspherecenters 3 3unitcells theatomicorderincrystallinesolidsindicatesthatsmallgroupsofatomsformarepetitivepattern thus indescribingcrystalstructures itisoftenconvenienttosubdivide 细分 thestructureintosmallrepeatentities 单元 calledunitcells unitcellsformostcrystalstructuresareparallelepipeds 平行六面体 orprisms棱柱体havingthreesetsofparallelfaces oneisdrawnwithintheaggregateofspheres figure3 1c whichinthiscasehappenstobeacube aunitcellischosentorepresentthesymmetryofthecrystalstructure whereinalltheatompositionsinthecrystalmaybegeneratedbytranslationsoftheunitcellintegraldistancesalongeachofitsedges thus theunitcellisthebasicstructuralunitorbuildingblockofthecrystalstructureanddefinesthecrystalstructurebyvirtueof由于itsgeometry几何形状andtheatompositionswithin convenienceusuallydictatesthatparallelepipedcornerscoincidewithcentersofthehardsphereatoms furthermore morethanasingleunitcellmaybechosenforaparticularcrystalstructure however wegenerallyusetheunitcellhavingthehighestlevelofgeometricalsymmetry 3 4metalliccrystalstructures theatomicbondinginthisgroupofmaterialsismetallic andthusnondirectionalinnature consequently therearenorestrictions 限制 astothenumberandpositionofnearest neighboratoms thisleadstorelativelylargenumbersofnearestneighborsanddenseatomicpackingsformostmetalliccrystalstructures also formetals usingthehardspheremodelforthecrystalstructure eachsphererepresentsanioncore table3 1presentstheatomicradiiforanumberofmetals threerelativelysimplecrystalstructuresarefoundformostofthecommonmetals face centeredcubic body centeredcubic andhexagonalclose packed theface centeredcubiccrystalstructure thecrystalstructurefoundformanymetalshasaunitcellofcubicgeometry withatomslocatedateachofthecornersandthecentersofallthecubefaces itisaptlycalledtheface centeredcubic fcc crystalstructure someofthefamiliarmetalshavingthiscrystalstructurearecopper aluminum silver andgold seealsotable3 1 figure3 1ashowsahardspheremodelforthefccunitcell whereasinfigure3 1btheatomcentersarerepresentedbysmallcirclestoprovideabetterperspectiveofatompositions theaggregateofatomsinfigure3 1crepresentsasectionofcrystalconsistingofmanyfccunitcells thesespheresorioncorestouchoneanotheracrossafacediagonal thecubeedgelengthaandtheatomicradiusrarerelatedthroughthisresultisobtainedasanexampleproblem forthefcccrystalstructure eachcorneratomissharedamongeightunitcells whereasaface centeredatombelongstoonlytwo therefore oneeighthofeachoftheeightcorneratomsandonehalfofeachofthesixfaceatoms oratotaloffourwholeatoms maybeassignedtoagivenunitcell thisisdepictedinfigure3 1a whereonlysphereportionsarerepresentedwithintheconfinesofthecube thecellcomprisesthevolumeofthecube whichisgeneratedfromthecentersofthecorneratomsasshowninthefigure cornerandfacepositionsarereallyequivalent thatis translationofthecubecornerfromanoriginalcorneratomtothecenterofafaceatomwillnotalterthecellstructure twootherimportantcharacteristicsofacrystalstructurearethecoordinationnumberandtheatomicpackingfactor apf formetals eachatomhasthesamenumberofnearest neighborortouchingatoms whichisthecoordinationnumber forface centeredcubics thecoordinationnumberis12 thismaybeconfirmedbyexaminationoffigure3 1a thefrontfaceatomhasfourcornernearest neighboratomssurroundingit fourfaceatomsthatareincontactfrombehind andfourotherequivalentfaceatomsresidinginthenextunitcelltothefront whichisnotshown theapfisthefractionofsolidspherevolumeinaunitcell assumingtheatomichardspheremodel or 3 2 forthefccstructure theatomicpackingfactoris0 74 whichisthemaximumpackingpossibleforspheresallhavingthesamediameter computationofthisapfisalsoincludedasanexampleproblem metalstypicallyhaverelativelylargeatomicpackingfactorstomaximizetheshielding遮蔽providedbythefreeelectroncloud thebody centeredcubiccrystalstructure anothercommonmetalliccrystalstructurealsohasacubicunitcellwithatomslocatedatalleightcornersandasingleatomatthecubecenter thisiscalledabody centeredcubic bcc crystalstructure acollectionofspheresdepicting描述thiscrystalstructureisshowninfigure3 2c whereasfigures3 2aand3 2barediagramsofbccunitcellswiththeatomsrepresentedbyhardsphereandreduced 缩小的 spheremodels respectively centerandcorneratomstouchoneanotheralongcubediagonals andunitcelllengthaandatomicradiusrarerelatedthroughchromium iron tungsten aswellasseveralothermetalslistedintable3 1exhibitabccstructure twoatomsareassociatedwitheachbccunitcell theequivalentofoneatomfromtheeightcorners eachofwhichissharedamongeightunitcells andthesinglecenteratom whichiswhollycontainedwithinitscell inaddition cornerandcenteratompositionsareequivalent thecoordinationnumberforthebcccrystalstructureis8 eachcenteratomhasasnearestneighborsitseightcorneratoms sincethecoordinationnumberislessforbccthanfcc soalsoistheatomicpackingfactorforbcclower 0 68versus0 74 thehexagonalclose packedcrystalstructure notallmetalshaveunitcellswithcubicsymmetry thefinalcommonmetalliccrystalstructuretobediscussedhasaunitcellthatishexagonal figure3 3ashowsareduced sphereunitcellforthisstructure whichistermedhexagonalclose packed hcp anassemblageofseveralhcpunitcellsispresentedinfigure3 3b thetopandbottomfacesoftheunitcellconsistofsixatomsthatformregularhexagons六边形andsurroundasingleatominthecenter anotherplanethatprovidesthreeadditionalatomstotheunitcellissituatedbetweenthetopandbottomplanes theatomsinthismidplanehaveasnearestneighborsatomsinbothoftheadjacenttwoplanes theequivalentofsixatomsiscontainedineachunitcell one sixthofeachofthe12topandbottomfacecorneratoms one halfofeachofthe2centerfaceatoms andallthe3midplaneinterioratoms ifaandcrepresent respectively theshortandlongunitcelldimensionsoffigure3 3a thec aratioshouldbe1 633 however forsomehcpmetalsthisratiodeviatesfromtheidealvalue thecoordinationnumberandtheatomicpackingfactorforthehcpcrystalstructurearethesameasforfcc 12and0 74 respectively thehcpmetalsincludecadmium magnesium titanium andzinc someofthesearelistedintable3 1 3 5densitycomputations metals aknowledgeofthecrystalstructureofametallicsolidpermitscomputationofitstheoreticaldensitythroughtherelationship 3 5 公式中n 单位晶胞中的原子数 a 原子量 vc 单位晶胞体积 na 阿夫加德罗常数 6 023 1023atom mol 3 6ceramiccrystalstructures becauseceramicsarecomposedofatleasttwoelements andoftenmore theircrystalstructuresaregenerallymorecomplexthanthoseformetals theatomicbondinginthesematerialsrangesfrompurelyionictototallycovalent manyceramicsexhibitacombinationofthesetwobondingtypes thedegreeofioniccharacterbeingdependentontheelectronegativitiesoftheatoms table3 2presentsthepercentioniccharacterforseveralcommonceramicmaterials thesevaluesweredeterminedusingequation2 10andtheelectronegativitiesinfigure2 7 forthoseceramicmaterialsforwhichtheatomicbondingispredominantlyionic thecrystalstructuresmaybethoughtofasbeingcomposedofelectricallychargedionsinsteadofatoms themetallicions orcations arepositivelycharged becausetheyhavegivenuptheirvalenceelectronstothenonmetallicions oranions whicharenegativelycharged twocharacteristicsofthecomponentionsincrystallineceramicmaterialsinfluencethecrystalstructure themagnitudeoftheelectricalchargeoneachofthecomponentions andtherelativesizesofthecationsandanions withregardtothefirstcharacteristic thecrystalmustbeelectricallyneutral thatis allthecationpositivechargesmustbebalancedbyanequalnumberofanionnegativecharges thechemicalformulaofacompoundindicatestheratioofcationstoanions orthecompositionthatachievesthischargebalance forexample incalciumfluoride eachcalciumionhasa 2charge ca2 andassociatedwitheachfluorineionisasinglenegativecharge f thus theremustbetwiceasmanyf asca2 ions whichisreflectedinthechemicalformulacaf2 thesecondcriterioninvolvesthesizesorionicradiiofthecationsandanions rcandra respectively becausethemetallicelementsgiveupelectronswhenionized cationsareordinarilysmallerthananions and consequently theratiorc raislessthanunity eachcationpreferstohaveasmanynearest neighboranionsaspossible theanionsalsodesireamaximumnumberofcationnearestneighbors stableceramiccrystalstructuresformwhenthoseanionssurroundingacationareallincontactwiththatcation asillustratedinfigure3 4 thecoordinationnumber i e numberofanionnearestneighborsforacation isrelatedtothecation anionradiusratio foraspecificcoordinationnumber thereisacritical 临界值 orminimumrc raratioforwhichthiscation anioncontactisestablished figure3 4 whichratiomaybedeterminedfrompuregeometricalconsiderations seeexampleproblem3 4 thecoordinationnumbersandnearest neighborgeometriesforvariousrc raratiosarepresentedintable3 3 forrc raratioslessthan0 155 theverysmallcationisbondedtotwoanionsinalinearmanner ifrc rahasavaluebetween0 155and0 225 thecoordinationnumberforthecationis3 thismeanseachcationissurroundedbythreeanionsintheformofaplanarequilateraltriangle withthecationlocatedinthecenter thecoordinationnumberis4forrc rabetween0 225and0 414 thecationislocatedatthecenterofatetrahedron withanionsateachofthefourcorners forrc rabetween0 414and0 732 thecationmaybethoughtofasbeingsituatedatthecenterofanoctahedronsurroundedbysixanions oneateachcorner asalsoshowninthetable thecoordinationnumberis8forrc rabetween0 732and1 0 withanionsatallcornersofacubeandacationpositionedatthecenter foraradiusratiogreaterthanunity thecoordinationnumberis12 themostcommoncoordinationnumbersforceramicmaterialsare4 6 and8 table3 4givestheionicradiiforseveralanionsandcationsthatarecommoninceramicmaterials ax typecrystalstructures someofthecommonceramicmaterialsarethoseinwhichthereareequalnumbersofcationsandanions theseareoftenreferredtoasaxcompounds whereadenotesthecationandxtheanion thereareseveraldifferentcrystalstructuresforaxcompounds eachisnormallynamedafteracommonmaterialthatassumestheparticularstructure rocksaltstructure perhapsthemostcommonaxcrystalstructureisthesodiumchloride nacl orrocksalt type thecoordinationnumberforbothcationsandanionsis6 andthereforethecation anionradiusratioisbetweenapproximately0 414and0 732 aunitcellforthiscrystalstructure figure3 5 isgeneratedfromanfccarrangementofanionswithonecationsituatedatthecubecenterandoneatthecenterofeachofthe12cubeedges anequivalentcrystalstructureresultsfromafacecenteredarrangementofcations thus therocksaltcrystalstructuremaybethoughtofastwointerpenetrating 相互穿插 fcclattices onecomposedofthecations theotherofanions someofthecommonceramicmaterialsthatformwiththiscrystalstructurearenacl mgo mns lif andfeo cesiumchloridestructure figure3 6showsaunitcellforthecesiumchloride cscl crystalstructure thecoordinationnumberis8forbothiontypes theanionsarelocatedateachofthecornersofacube whereasthecubecenterisasinglecation interchangeofanionswithcations andviceversa producesthesamecrystalstructure thisisnotabcccrystalstructurebecauseionsoftwodifferentkindsareinvolved zincblendestructure athirdaxstructureisoneinwhichthecoordinationnumberis4 thatis allionsaretetrahedrallycoordinated thisiscalledthezincblende orsphalerite structure afterthemineralogical 矿物学的 termforzincsulfide zns aunitcellispresentedinfigure3 7 allcornerandfacepositionsofthecubiccellareoccupiedbysatoms whiletheznatomsfillinteriortetrahedralpositions anequivalentstructureresultsifznandsatompositionsarereversed thus eachznatomisbondedtofoursatoms andviceversa mostoftentheatomicbondingishighlycovalentincompoundsexhibitingthiscrystalstructure table3 2 whichincludezns znte andsic amxp typecrystalstructures ifthechargesonthecationsandanionsarenotthesame acompoundcanexistwiththechemicalformulaamxp wheremand orp1 anexamplewouldbeax2 forwhichacommoncrystalstructureisfoundinfluorite caf2 theionicradiiratiorc raforcaf2isabout0 8which accordingtotable3 3 givesacoordinationnumberof8 calciumionsarepositionedatthecentersofcubes withfluorineionsatthecorners thechemicalformulashowsthatthereareonlyhalfasmanyca2 ionsasf ions andthereforethecrystalstructurewouldbesimilartocscl figure3 6 exceptthatonlyhalfthecentercubepositionsareoccupiedbyca2 ions oneunitcellconsistsofeightcubes asindicatedinfigure3 8 othercompoundsthathavethiscrystalstructureincludeuo2 puo2 andtho2 ambnxp typecrystalstructures itisalsopossibleforceramiccompoundstohavemorethanonetypeofcation fortwotypesofcations representedbyaandb theirchemicalformulamaybedesignatedasambnxp bariumtitanate batio3 havingbothba2 andti4 cations fallsintothisclassification thismaterialhasaperovskite钙钛矿crystalstructureandratherinterestingelectromechanicalpropertiestobediscussedlater attemperaturesabove120 248f thecrystalstructureiscubic aunitcellofthisstructureisshowninfigure3 9 ba2 ionsaresituatedatalleightcornersofthecubeandasingleti4 isatthecubecenter witho2 ionslocatedatthecenterofeachofthesixfaces table3 5summarizestherocksalt cesiumchloride zincblende fluorite andperovskitecrystalstructuresintermsofcation anionratiosandcoordinationnumbers andgivesexamplesforeach ofcourse manyotherceramiccrystalstructuresarepossible 3 7densitycomputations ceramics itispossibletocomputethetheoreticaldensityofacrystallineceramicmaterialfromunitcelldatainamannersimilartothatdescribedinsection3 5formetals inthiscasethedensitymaybedeterminedusingamodifiedformofequation3 5 asfollows 公式中 n 单位晶胞中的分子数 ac 化学式中所有阳离子原子量的和 aa 化学式中所有阴离子原子量的和 vc 单位晶胞体积 na 阿佛加德罗常数 3 6 3 8silicateceramics silicatesarematerialscomposedprimarilyofsiliconandoxygen thetwomostabundantelementsintheearth scrust consequently thebulkofsoils rocks clays andsandcomeunderthesilicateclassification ratherthancharacterizingthecrystalstructuresofthesematerialsintermsofunitcells itismoreconvenienttousevariousarrangementsofansio44 tetrahedron四面体 figure3 10 eachatomofsiliconisbondedtofouroxygenatoms whicharesituatedatthecornersofthetetrahedron thesiliconatomispositionedatthecenter sincethisisthebasicunitofthesilicates itisoftentreatedasan