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1、C h a p t e r 3 / Structures of Metals and CeramicsWhy Study Structures of Metals and Ceramics?The properties of some materials are directly related to their crystal structures. For example, pure and undeformed magnesium and beryllium, having one crystal structure, are much more brittle (i.e., fract
2、ure at lower degrees of deformation) than are pure and undeformed metals such as gold and silver that have yet another crystal structure (see Section 8.5). Furthermore,significantpropertydifferences exist between crystallineandnoncrystallinematerialshavingthesamecomposition.Forexample,noncrystalline
3、 ceramics and polymersnormally are optically transparent; thesamematerialsincrystalline(orsemicrystalline)formtendtobeopaqueor,atbest,translucent.同素异型同素异型晶系晶系晶格参数晶格参数无定形的无定形的晶体晶体密勒指数密勒指数阴离子阴离子衍射衍射非晶体非晶体各向异性各向异性面心立方面心立方八面体位置八面体位置致密度致密度颗粒颗粒多晶体多晶体体心立方体心立方晶粒界晶粒界类质异象类质异象 布拉格定律布拉格定律密排六方密排六方单晶体单晶体阳离子阳离子各向同
4、性各向同性四面体位置四面体位置配位数配位数晶格晶格单位晶胞单位晶胞晶体结构晶体结构L e a r n i n g O b j e c t i v e s After studying this chapter you should be able to do the following:1. Describe the difference in atomic/molecular structure between crystalline and noncrystalline materials.2. Draw unit cells for face-centered cubic, body-c
5、entered cubic, and hexagonal close-packed crystal structures.3. Derive the relationships between unit cell edge length and atomic radius for face-centered cubic and body-centered cubic crystal structures.4. Compute the densities for metals having face-centered cubic and body-centered cubic crystal s
6、tructures given their unit cell dimensions.5. Sketch/describe unit cells for sodium chloride, cesium chloride, zinc blende, diamond cubic, fluorite, and perovskite crystal structures. Do likewise for the atomic structures of graphite and a silica glass6. Given the chemical formula for a ceramic comp
7、ound, the ionic radii of its component ions, determine the crystal structure.7. Given three direction index integers, sketch the direction corresponding to these indices within a unit cell.8. Specify the Miller indices for a plane that has been drawn within a unit cell.9. Describe how face-centered
8、cubic and hexagonal close-packed crystal structures may be generated by the stacking of close-packed planes of atoms. Do the same for the sodium chloride crystal structure in terms of close-packed planes of anions.10. Distinguish between single crystals and polycrystalline materials. 11. Define isot
9、ropy and anisotropy with respect to material properties.3.1 INTRODUCTIONChapter2wasconcernedprimarilywiththevarioustypesofatomicbonding,whicharedeterminedbytheelectronstructureoftheindividualatoms.Thepresentdiscussionisdevotedtothenextlevelofthestructureofmaterials,specifically,tosomeofthearrangemen
10、tsthatmaybeassumedbyatomsinthesolidstate.Withinthisframework（结构）,conceptsofcrystallinityandnoncrystallinityareintroduced.Forcrystallinesolidsthenotion（ 概 念 ） ofcrystalstructureispresented,specifiedintermsofaunitcell.Crystal structures found in bothmetalsandceramicsarethendetailed,alongwiththescheme（
11、构型）bywhichcrystallographic（晶体学 的 ） directions and planes areexpressed.Singlecrystals,polycrystalline,andnoncrystallinematerialsareconsidered.CRYSTALSTRUCTURES3.2 FUNDAMENTAL CONCEPTSSolid materials may be classifiedaccordingtotheregularitywithwhichatoms or ions are arranged withrespecttooneanother.A
12、crystalline materialisoneinwhichtheatomsaresituatedinarepeatingor periodic array over large atomicdistances; that is, long-range orderexists,suchthatuponsolidification（固化）, the atoms will positionthemselves in a repetitive three-dimensionalpattern（构图）,inwhicheach atom is bonded to its nearest-neighb
13、oratoms.All metals, many ceramic materials,and certain polymers form crystallinestructures under normal solidificationconditions. For those that do notcrystallize,thislong-rangeatomicorderis absent; these noncrystalline oramorphous materials are discussedbrieflyattheendofthischapter.Someofthepropert
14、iesofcrystallinesolidsdependonthecrystal structure ofthematerial,themannerinwhichatoms,ions,ormoleculesarespatiallyarranged（空间排列）.Thereisanextremelylargenumberofdifferentcrystalstructuresallhavinglong-rangeatomicorder;thesevaryfromrelativelysimplestructuresformetals,toexceedinglycomplexones,asdispla
15、yedbysomeoftheceramicandpolymericmaterials.Thepresentdiscussiondealswithseveralcommonmetallicandceramiccrystalstructures.Thenextchapterisdevotedtostructuresforpolymers.Whendescribingcrystallinestructures,atoms(orions)arethoughtofasbeingsolidsphereshavingwell-defineddiameters.Thisistermedtheatomic ha
16、rd sphere model inwhichspheresrepresentingnearest-neighboratomstouchoneanother.Anexampleofthehardspheremodelfor the atomic arrangement found insomeofthecommonelementalmetalsisdisplayed（显示）inFigure3.1c.Inthis particular case all the atoms areidentical.Sometimesthetermlattice isusedinthe context（ 课 文
17、） of crystalstructures; in this sense latticemeans a three-dimensional array ofpointscoinciding（相同）withatompositions(orspherecenters).3.3 UNIT CELLSTheatomicorderincrystallinesolidsindicatesthatsmallgroupsofatomsformarepetitivepattern.Thus,indescribingcrystalstructures,itisoftenconvenienttosubdivide
18、（细分）thestructureintosmallrepeatentities（单元）calledunit cells. Unitcellsformostcrystalstructuresareparallelepipeds（平行六面体）orprisms棱柱体havingthreesetsofparallelfaces;oneisdrawnwithintheaggregateofspheres(Figure3.1c),whichinthiscasehappenstobeacube.Aunitcellischosentorepresentthesymmetryofthecrystalstruct
19、ure,whereinalltheatompositionsinthecrystalmaybegeneratedbytranslationsoftheunitcellintegraldistancesalongeachofitsedges.Thus,theunitcellisthebasicstructuralunitorbuildingblockofthecrystalstructureanddefinesthecrystalstructurebyvirtueof由于itsgeometry几何形状andtheatompositionswithin.Convenienceusuallydict
20、atesthatparallelepipedcornerscoincidewithcentersofthehardsphereatoms.Furthermore,morethanasingleunitcellmaybechosenforaparticularcrystalstructure;however,wegenerallyusetheunitcellhavingthehighestlevelofgeometricalsymmetry.3.4 METALLIC CRYSTAL STRUCTURESTheatomicbondinginthisgroupofmaterialsismetalli
21、c,andthusnondirectionalinnature.Consequently,therearenorestrictions（限制）astothenumberandpositionofnearest-neighboratoms;thisleadstorelativelylargenumbersofnearestneighborsanddenseatomicpackingsformostmetalliccrystalstructures.Also,formetals,usingthehardspheremodelforthecrystalstructure,eachsphererepr
22、esentsanioncore.Table3.1presentstheatomicradiiforanumberofmetals.Threerelativelysimplecrystalstructuresarefoundformostofthecommonmetals:face-centeredcubic,body-centeredcubic,andhexagonalclose-packed.THE FACE-CENTERED CUBIC CRYSTAL STRUCTUREThecrystalstructurefoundformanymetalshasaunitcellofcubicgeom
23、etry,withatomslocatedateachofthecornersandthecentersofallthecubefaces.Itisaptlycalledtheface-centered cubic (FCC) crystalstructure.Someofthefamiliarmetalshavingthiscrystalstructurearecopper,aluminum,silver,andgold(seealsoTable3.1).Figure3.1a showsahardspheremodelfortheFCCunitcell,whereasinFigure3.1b
24、 theatomcentersarerepresentedbysmallcirclestoprovideabetterperspectiveofatompositions.TheaggregateofatomsinFigure3.1c representsasectionofcrystalconsistingofmanyFCCunitcells.Thesespheresorioncorestouchoneanotheracrossafacediagonal;thecubeedgelengtha andtheatomicradiusR arerelatedthroughThisresultiso
25、btainedasanexampleproblem.FortheFCCcrystalstructure,eachcorneratomissharedamongeightunitcells,whereasaface-centeredatombelongstoonlytwo.Therefore,oneeighthofeachoftheeightcorneratomsandonehalfofeachofthesixfaceatoms,oratotaloffourwholeatoms,maybeassignedtoagivenunitcell.ThisisdepictedinFigure3.1a,wh
26、ereonlysphereportionsarerepresentedwithintheconfinesofthecube.Thecellcomprisesthevolumeofthecube,whichisgeneratedfromthecentersofthecorneratomsasshowninthefigure.Cornerandfacepositionsarereallyequivalent;thatis,translationofthecubecornerfromanoriginalcorneratomtothecenterofafaceatomwillnotalterthece
27、llstructure.Twootherimportantcharacteristicsofacrystalstructurearethecoordination number andtheatomic packing factor (APF).Formetals,eachatomhasthesamenumberofnearest-neighborortouchingatoms,whichisthecoordinationnumber.Forface-centeredcubics,thecoordinationnumberis12.Thismaybeconfirmedbyexamination
28、ofFigure3.1a;thefrontfaceatomhasfourcornernearest-neighboratomssurroundingit,fourfaceatomsthatareincontactfrombehind,andfourotherequivalentfaceatomsresidinginthenextunitcelltothefront,whichisnotshown.TheAPFisthefractionofsolidspherevolumeinaunitcell,assumingtheatomichardspheremodel,or（3.2）FortheFCCs
29、tructure,theatomicpackingfactoris0.74,whichisthemaximumpackingpossibleforspheresallhavingthesamediameter.ComputationofthisAPFisalsoincludedasanexampleproblem.Metalstypicallyhaverelativelylargeatomicpackingfactorstomaximizetheshielding遮蔽providedbythefreeelectroncloud.THE BODY-CENTERED CUBIC CRYSTAL S
30、TRUCTUREAnothercommonmetalliccrystalstructurealsohasacubicunitcellwithatomslocatedatalleightcornersandasingleatomatthecubecenter.Thisiscalledabody-centered cubic (BCC) crystalstructure.Acollectionofspheresdepicting描述thiscrystalstructureisshowninFigure3.2c,whereasFigures3.2a and3.2b arediagramsofBCCu
31、nitcellswiththeatomsrepresentedbyhardsphereandreduced（缩小的）-spheremodels,respectively.Centerandcorneratomstouchoneanotheralongcubediagonals,andunitcelllengtha andatomicradiusR arerelatedthroughChromium,iron,tungsten,aswellasseveralothermetalslistedinTable3.1exhibitaBCCstructure.Twoatomsareassociatedw
32、itheachBCCunitcell:theequivalentofoneatomfromtheeightcorners,eachofwhichissharedamongeightunitcells,andthesinglecenteratom,whichiswhollycontainedwithinitscell.Inaddition,cornerandcenteratompositionsareequivalent.ThecoordinationnumberfortheBCCcrystalstructureis8;eachcenteratomhasasnearestneighborsits
33、eightcorneratoms.SincethecoordinationnumberislessforBCCthanFCC,soalsoistheatomicpackingfactorforBCClower0.68versus0.74.THE HEXAGONAL CLOSE-PACKED CRYSTAL STRUCTURENotallmetalshaveunitcellswithcubicsymmetry;thefinalcommonmetalliccrystalstructuretobediscussedhasaunitcellthatishexagonal.Figure3.3a show
34、sareduced-sphereunitcellforthisstructure,whichistermedhexagonal close-packed (HCP); anassemblageofseveralHCPunitcellsispresentedinFigure3.3b.Thetopandbottomfacesoftheunitcellconsistofsixatomsthatformregularhexagons六边形andsurroundasingleatominthecenter.Anotherplanethatprovidesthreeadditionalatomstothe
35、unitcellissituatedbetweenthetopandbottomplanes.Theatomsinthismidplanehaveasnearestneighborsatomsinbothoftheadjacenttwoplanes.Theequivalentofsixatomsiscontainedineachunitcell;one-sixthofeachofthe12topandbottomfacecorneratoms,one-halfofeachofthe2centerfaceatoms,andallthe3midplaneinterioratoms.Ifa andc
36、 represent,respectively,theshortandlongunitcelldimensionsofFigure3.3a,thec/a ratioshouldbe1.633;however,forsomeHCPmetalsthisratiodeviatesfromtheidealvalue.ThecoordinationnumberandtheatomicpackingfactorfortheHCPcrystalstructurearethesameasforFCC:12and0.74,respectively.TheHCPmetalsincludecadmium,magne
37、sium,titanium,andzinc;someofthesearelistedinTable3.1.3.5 DENSITY COMPUTATIONSMETALSAknowledgeofthecrystalstructureofametallicsolidpermitscomputationofitstheoreticaldensitythroughtherelationship（3.53.5）公式中公式中n n单位晶胞中的原子数；单位晶胞中的原子数；A A原子量；原子量；VcVc单位晶胞体积；单位晶胞体积；NANA阿夫加德罗常数（阿夫加德罗常数（6.023106.023102323ato
38、m/molatom/mol）3.6 CERAMIC CRYSTAL STRUCTURESBecauseceramicsarecomposedofatleasttwoelements,andoftenmore,theircrystalstructuresaregenerallymorecomplexthanthoseformetals.Theatomicbondinginthesematerialsrangesfrompurelyionictototallycovalent;manyceramicsexhibitacombinationofthesetwobondingtypes,thedegr
39、eeofioniccharacterbeingdependentontheelectronegativitiesoftheatoms.Table3.2presentsthepercentioniccharacterforseveralcommonceramicmaterials;thesevaluesweredeterminedusingEquation2.10andtheelectronegativitiesinFigure2.7.Forthoseceramicmaterialsforwhichtheatomicbondingispredominantlyionic,thecrystalst
40、ructuresmaybethoughtofasbeingcomposedofelectricallychargedionsinsteadofatoms.Themetallicions,orcations, arepositivelycharged,becausetheyhavegivenuptheirvalenceelectronstothenonmetallicions,oranions, whicharenegativelycharged.Twocharacteristicsofthecomponentionsincrystallineceramicmaterialsinfluencet
41、hecrystalstructure:themagnitudeoftheelectricalchargeoneachofthecomponentions,andtherelativesizesofthecationsandanions.Withregardtothefirstcharacteristic,thecrystalmustbeelectricallyneutral;thatis,allthecationpositivechargesmustbebalancedbyanequalnumberofanionnegativecharges.Thechemicalformulaofacomp
42、oundindicatestheratioofcationstoanions,orthecompositionthatachievesthischargebalance.Forexample,incalciumfluoride,eachcalciumionhasa+2charge(Ca2+),andassociatedwitheachfluorineionisasinglenegativecharge(F-).Thus,theremustbetwiceasmanyF-asCa2+ions,whichisreflectedinthechemicalformulaCaF2.Thesecondcri
43、terioninvolvesthesizesorionicradiiofthecationsandanions,rCandrA,respectively.Becausethemetallicelementsgiveupelectronswhenionized,cationsareordinarilysmallerthananions,and,consequently,theratiorC/rAislessthanunity.Eachcationpreferstohaveasmanynearest-neighboranionsaspossible.Theanionsalsodesireamaxi
44、mumnumberofcationnearestneighbors.Stableceramiccrystalstructuresformwhenthoseanionssurroundingacationareallincontactwiththatcation,asillustratedinFigure3.4.Thecoordinationnumber(i.e.,numberofanionnearestneighborsforacation)isrelatedtothecationanionradiusratio.Foraspecificcoordinationnumber,thereisac
45、ritical(临界值)orminimumrC/rAratioforwhichthiscationanioncontactisestablished(Figure3.4),whichratiomaybedeterminedfrompuregeometricalconsiderations(seeExampleProblem3.4).Thecoordinationnumbersandnearest-neighborgeometriesforvariousrC/rAratiosarepresentedinTable3.3.ForrC/rAratioslessthan0.155,theverysma
46、llcationisbondedtotwoanionsinalinearmanner.IfrC/rAhasavaluebetween0.155and0.225,thecoordinationnumberforthecationis3.Thismeanseachcationissurroundedbythreeanionsintheformofaplanarequilateraltriangle,withthecationlocatedinthecenter.Thecoordinationnumberis4forrC/rAbetween0.225and0.414;thecationislocat
47、edatthecenterofatetrahedron,withanionsateachofthefourcorners.ForrC/rAbetween0.414and0.732,thecationmaybethoughtofasbeingsituatedatthecenterofanoctahedronsurroundedbysixanions,oneateachcorner,asalsoshowninthetable.Thecoordinationnumberis8forrC/rAbetween0.732and1.0,withanionsatallcornersofacubeandacat
48、ionpositionedatthecenter.Foraradiusratiogreaterthanunity,thecoordinationnumberis12.Themostcommoncoordinationnumbersforceramicmaterialsare4,6,and8.Table3.4givestheionicradiiforseveralanionsandcationsthatarecommoninceramicmaterials.AX-TYPE CRYSTAL STRUCTURESSomeofthecommonceramicmaterialsarethoseinwhi
49、chthereareequalnumbersofcationsandanions.TheseareoftenreferredtoasAXcompounds,whereAdenotesthecationandXtheanion.ThereareseveraldifferentcrystalstructuresforAXcompounds;eachisnormallynamedafteracommonmaterialthatassumestheparticularstructure.Rock Salt StructurePerhapsthemostcommonAXcrystalstructurei
50、sthesodium chloride (NaCl),orrock salt, type.Thecoordinationnumberforbothcationsandanionsis6,andthereforethecationanionradiusratioisbetweenapproximately0.414and0.732.Aunitcellforthiscrystalstructure(Figure3.5)isgeneratedfromanFCCarrangementofanionswithonecationsituatedatthecubecenterandoneatthecente
51、rofeachofthe12cubeedges.Anequivalentcrystalstructureresultsfromafacecenteredarrangementofcations.Thus,therocksaltcrystalstructuremaybethoughtofastwointerpenetrating(相互穿插)FCClattices,onecomposedofthecations,theotherofanions.SomeofthecommonceramicmaterialsthatformwiththiscrystalstructureareNaCl,MgO,Mn
52、S,LiF,andFeO.Cesium Chloride StructureFigure3.6showsaunitcellforthecesium chloride (CsCl)crystalstructure;thecoordinationnumberis8forbothiontypes.Theanionsarelocatedateachofthecornersofacube,whereasthecubecenterisasinglecation.Interchangeofanionswithcations,andviceversa,producesthesamecrystalstructu
53、re.Thisisnot aBCCcrystalstructurebecauseionsoftwodifferentkindsareinvolved.Zinc Blende StructureAthirdAXstructureisoneinwhichthecoordinationnumberis4;thatis,allionsaretetrahedrallycoordinated.Thisiscalledthezinc blende, orsphalerite, structure,afterthemineralogical(矿物学的)termforzincsulfide(ZnS).Aunit
54、cellispresentedinFigure3.7;allcornerandfacepositionsofthecubiccellareoccupiedbySatoms,whiletheZnatomsfillinteriortetrahedralpositions.AnequivalentstructureresultsifZnandSatompositionsarereversed.Thus,eachZnatomisbondedtofourSatoms,andviceversa.Mostoftentheatomicbondingishighlycovalentincompoundsexhi
55、bitingthiscrystalstructure(Table3.2),whichincludeZnS,ZnTe,andSiC.AmXp-TYPE CRYSTAL STRUCTURESIfthechargesonthecationsandanionsarenotthesame,acompoundcanexistwiththechemicalformulaAmXp ,wherem and/orp 1.AnexamplewouldbeAX2,forwhichacommoncrystalstructureisfoundinfluorite (CaF2).TheionicradiiratiorC/r
56、AforCaF2isabout0.8which,accordingtoTable3.3,givesacoordinationnumberof8.Calciumionsarepositionedatthecentersofcubes,withfluorineionsatthecorners.ThechemicalformulashowsthatthereareonlyhalfasmanyCa2+ionsasF-ions,andthereforethecrystalstructurewouldbesimilartoCsCl(Figure3.6),exceptthatonlyhalfthecente
57、rcubepositionsareoccupiedbyCa2+ions.Oneunitcellconsistsofeightcubes,asindicatedinFigure3.8.OthercompoundsthathavethiscrystalstructureincludeUO2,PuO2,andThO2.AmBnXp-TYPE CRYSTAL STRUCTURESItisalsopossibleforceramiccompoundstohavemorethanonetypeofcation;fortwotypesofcations(representedbyAandB),theirch
58、emicalformulamaybedesignatedasAmBnXp .Bariumtitanate(BaTiO3),havingbothBa2+andTi4+cations,fallsintothisclassification.Thismaterialhasaperovskite钙钛矿 crystal structure andratherinterestingelectromechanicalpropertiestobediscussedlater.Attemperaturesabove120(248F),thecrystalstructureiscubic.Aunitcelloft
59、hisstructureisshowninFigure3.9;Ba2+ionsaresituatedatalleightcornersofthecubeandasingleTi4+isatthecubecenter,withO2-ionslocatedatthecenterofeachofthesixfaces.Table3.5summarizestherocksalt,cesiumchloride,zincblende,fluorite,andperovskitecrystalstructuresintermsofcationanionratiosandcoordinationnumbers
60、,andgivesexamplesforeach.Ofcourse,manyotherceramiccrystalstructuresarepossible.结 构 代号 结构名称 配位数负离子堆积方式正离子位置 化合物举例AB CsCl 8 ： 8 AB简单立方全部立方体空隙RbCl， RbBr， RbI，CsCI，SsBr，CsI NaCl (岩盐) 6 ： 6 AB面心立方全部八面体空隙NaCI，KCI，LiF，KBr，MgO，CaO，SrO，BaO，CdO，FeO，CoO，NiO 闪锌矿 (ZnS) 4 ： 4 AB面心立方1/2四面体空隙ZnS，-SiC，GaAs，AlP，InSbA
61、B2 萤 石 (CaF2) 8 ：4 AB2简单立方12立方体空隙CaF2，Ce02， U02，Zr02，Hf02，Np02，Pu02，Am02 硅石型 (Si02) 4 ：2 AB2互联的四面体-Si02 AB03 钙钛矿(CaTi03)12：6：6 AB03立方密堆14八面体空隙(B)CaTi03，SrTiO3，SrSn03，SrZrO3，SrHf03，BaTiO3 AB204正尖晶石(MgAl204)4：6：4 AB204立方密堆1 18 8四面体空四面体空隙隙(A)(A)1 12 2八面体空八面体空隙隙(B)(B)FeAl204， ZnAl204，Mgall04B(AB)O4反尖晶石4
62、：6：4B(AB)O4立方密堆1 18 8四面体空四面体空隙隙(B)(B)1 12 2八面体空八面体空隙隙(A(A，B)B)FeMgFe04，MgTiMg043.7 DENSITY COMPUTATIONSCERAMICSItispossibletocomputethetheoreticaldensityofacrystallineceramicmaterialfromunitcelldatainamannersimilartothatdescribedinSection3.5formetals.Inthiscasethedensitymaybedeterminedusingamodified
63、formofEquation3.5,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)3.8 SILICATE CERAMICSSilicatesarematerialscomposedprimarilyofsiliconandoxygen,thetwomostabundantelementsintheearthscrust;consequently,thebulkofsoils,rocks,clays,andsandcomeunderthesilicateclassifica
64、tion.Ratherthancharacterizingthecrystalstructuresofthesematerialsintermsofunitcells,itismoreconvenienttousevariousarrangementsofanSiO44-tetrahedron四面体(Figure3.10).Eachatomofsiliconisbondedtofouroxygenatoms,whicharesituatedatthecornersofthetetrahedron;thesiliconatomispositionedatthecenter.Sincethisis
65、thebasicunitofthesilicates,itisoftentreatedasanegativelychargedentity.OftenthesilicatesarenotconsideredtobeionicbecausethereisasignificantcovalentcharactertotheinteratomicSiObonds(Table3.2),whichbondsaredirectionalandrelativelystrong.RegardlessofthecharacteroftheSiObond,thereisa4chargeassociatedwith
66、everySiO44-tetrahedron,sinceeachofthefouroxygenatomsrequiresanextraelectrontoachieveastableelectronicstructure.VarioussilicatestructuresarisefromthedifferentwaysinwhichtheSiO44-unitscanbecombinedintoone-,two-,andthree-dimensionalarrangements.SILICAChemically,themostsimplesilicatematerialissilicondio
67、xide,orsilica(SiO2).Structurally,itisathree-dimensionalnetworkthatisgeneratedwheneverycorneroxygenatomineachtetrahedronissharedbyadjacenttetrahedra.Thus,thematerialiselectricallyneutralandallatomshavestableelectronicstructures.UnderthesecircumstancestheratioofSitoOatomsis1:2,asindicatedbythechemical
68、formula.Ifthesetetrahedraarearrayedinaregularandorderedmanner,acrystallinestructureisformed.Therearethreeprimarypolymorphiccrystallineformsofsilica:quartz(石英）,cristobalite（方石英）(Figure3.11),andtridymite（鳞石英）.Theirstructuresarerelativelycomplicated,andcomparativelyopen;thatis,theatomsarenotcloselypack
69、edtogether.Asaconsequence,thesecrystallinesilicashaverelativelylowdensities;forexample,atroomtemperaturequartzhasadensityofonly2.65g/cm3.ThestrengthoftheSiOinteratomicbondsisreflectedinarelativelyhighmeltingtemperature,1710(3110F).Silicacanalsobemadetoexistasanoncrystallinesolidorglass;itsstructurei
70、sdiscussedinSection3.20.3.9 CARBONCarbonisanelementthatexistsinvariouspolymorphicforms,aswellasintheamorphousstate.Thisgroupofmaterialsdoesnotreallyfallwithinanyoneofthetraditionalmetal,ceramic,polymerclassificationschemes.However,ithasbeendecidedtodiscussthesematerialsinthischaptersincegraphite,one
71、ofthepolymorphicforms,issometimesclassifiedasaceramic.Thistreatmentfocusesonthestructuresofgraphiteanddiamondandthenewfullerenes富勒烯.ThecharacteristicsandcurrentandpotentialusesofthesematerialsarediscussedinSection13.11.DIAMONDDiamondisametastablecarbonpolymorphatroomtemperatureandatmosphericpressure
72、.Itscrystalstructureisavariantofthezincblende,inwhichcarbonatomsoccupyallpositions(bothZnandS),asindicatedintheunitcellshowninFigure3.16.Thus,eachcarbonbondstofourothercarbons,andthesebondsaretotallycovalent.Thisisappropriatelycalledthediamond cubic crystalstructure,whichisalsofoundforotherGroupIVAe
73、lementsintheperiodictablee.g.,germanium,silicon,andgraytin,below13(55F).GRAPHITEGraphitehasacrystalstructure(Figure3.17)distinctlydifferentfromthatofdiamondandisalsomorestablethandiamondatambienttemperatureandpressure.Thegraphitestructureiscomposedoflayersofhexagonally六边形arrangedcarbonatoms;withinth
74、elayers,eachcarbonatomisbondedtothreecoplanarneighboratomsbystrongcovalentbonds.ThefourthbondingelectronparticipatesinaweakvanderWaalstypeofbondbetweenthelayers.3.10 POLYMORPHISM AND ALLOTROPYSomemetals,aswellasnonmetals,mayhavemorethanonecrystalstructure,aphenomenonknownaspolymorphism（同质多晶）（同质多晶）.
75、Whenfoundinelementalsolids,theconditionisoftentermedallotropy（同素异型）（同素异型）. Theprevailingcrystalstructuredependsonboththetemperatureandtheexternalpressure.Onefamiliarexampleisfoundincarbonasdiscussedintheprevioussection:graphiteisthestablepolymorphatambientconditions,whereasdiamondisformedatextremely
76、highpressures.Also,pureironhasaBCCcrystalstructureatroomtemperature,whichchangestoFCCironat912(1674F).Mostoftenamodificationofthedensityandotherphysicalpropertiesaccompaniesapolymorphictransformation.3.11 CRYSTAL SYSTEMSSincetherearemanydifferentpossiblecrystalstructures,itissometimesconvenienttodiv
77、idethemintogroupsaccordingtounitcellconfigurationsand/oratomicarrangements.Onesuchschemeisbasedontheunitcellgeometry,thatis,theshapeoftheappropriateunitcellparallelepiped平行六面体withoutregardtotheatomicpositionsinthecell.nWithin this framework构架, an x, y, z coordinate坐标 system is established with its o
78、rigin at one of the unit cell corners; each of the x, y, and z axes coincides with one of the three parallelepiped edges that extend from this corner, as illustrated in Figure 3.19. Theunitcellgeometryiscompletelydefinedintermsofsixparameters:thethreeedgelengthsa,b,andc,andthethreeinteraxialangles,a
79、nd.TheseareindicatedinFigure3.19,andaresometimestermedthelattice parameters ofacrystalstructure.Onthisbasistherearefoundcrystalshavingsevendifferentpossiblecombinationsofa,b,andc,and,and,eachofwhichrepresentsadistinctcrystal system.Thesesevencrystalsystemsarecubic,tetragonal（四方，正方）,hexagonal,orthorh
80、ombic（正交）,rhombohedral（菱方）,monoclinic（单斜）,andtriclinic（三斜）.ThelatticeparameterrelationshipsandunitcellsketchesforeacharerepresentedinTable3.6.Thecubicsystem,forwhicha =b =c and90,hasthegreatestdegreeofsymmetry.Leastsymmetryisdisplayedbythetriclinicsystem,sincea b c and.Fromthediscussionofmetalliccry
81、stalstructures,itshouldbeapparentthatbothFCCandBCCstructuresbelongtothecubiccrystalsystem,whereasHCPfallswithinhexagonal.Theconventionalhexagonalunitcellreallyconsistsofthreeparallelepipeds（平行六面体）situatedasshowninTable3.6.CRYSTALLOGRAPHICDIRECTIONSANDPLANESWhendealingwithcrystallinematerials,itoften
82、becomesnecessarytospecifysomeparticularcrystallographicplaneofatomsoracrystallographicdirection.Labelingconventions常规havebeenestablishedinwhichthreeintegersorindices指数areusedtodesignatedirectionsandplanes.Thebasisfordeterminingindexvaluesistheunitcell,withacoordinatesystemconsistingofthree(x,y,andz)
83、axessituatedatoneofthecornersandcoincidingwiththeunitcelledges,asshowninFigure3.19.Forsomecrystalsystemsnamely,hexagonal,rhombohedral,monoclinic,andtriclinicthethreeaxesarenot mutuallyperpendicular垂直,asinthefamiliarCartesiancoordinatescheme.3.12 CRYSTALLOGRAPHIC DIRECTIONS Acrystallographicdirection
84、isdefinedasalinebetweentwopoints,oravector.Thefollowingstepsareutilizedinthedeterminationofthethreedirectionalindices.1. Avectorofconvenientlengthispositionedsuchthatitpassesthroughtheoriginofthecoordinatesystem.Anyvectormaybetranslatedthroughoutthecrystallatticewithoutalteration,ifparallelism平行isma
85、intained.2. Thelengthofthevectorprojection投影oneachofthethreeaxesisdetermined;these are measured in terms of the unit cell dimensions a,b,and c.3. Thesethreenumbersaremultipliedordividedbyacommonfactortoreducethemtothesmallestintegervalues.4. Thethreeindices,notseparatedbycommas,areenclosedinsquarebr
86、ackets,thus:uvw.Theu,v,andw integerscorrespondtothereducedprojectionsalongthex,y,andz axes,respectively.Foreachofthethreeaxes,therewillexistbothpositiveandnegativecoordinates.Thusnegativeindicesarealsopossible,whicharerepresentedbyabarovertheappropriateindex.Forexample,the11directionwouldhaveacompon
87、entinthey direction.Also,changingthesignsofallindicesproducesanantiparallel反direction;thatis,1isdirectlyoppositeto11.Ifmorethanonedirectionorplaneistobespecifiedforaparticularcrystalstructure,itisimperative必需的forthemaintainingofconsistencythatapositivenegativeconvention,onceestablished,notbechanged.
88、The100,110,and111directionsarecommonones;theyaredrawnintheunitcellshowninFigure3.20.补充说明：（本书外内容）当然，在确定晶向指数时，坐标原点不一定非选在晶向上不可。若原点不在待标晶向上，那就需要找出该晶向上两点的坐标(x1,y1,z1)和(x2,y2,z2)，然后将(x2-x1),(y2-y1),(z2-z1)三个数化成互质整数u，v，w，并使之满足u:v:w=(x2-x1):(y2-y1):(z2-z1)。举例习题3.52(书71页）Forsomecrystalstructures,severalnonpar
89、alleldirectionswithdifferentindicesareactuallyequivalent等价的;thismeansthatthespacingofatomsalongeachdirectionisthesame.Forexample,incubiccrystals,allthedirectionsrepresentedbythefollowingindicesareequivalent:100,00、010、00、001、and00.Asaconvenience,equivalentdirectionsaregroupedtogetherintoafamily,whic
90、hareenclosedinanglebrackets,thus:.Furthermore,directionsincubiccrystalshavingthesameindiceswithoutregardtoorderorsign,forexample,123and,areequivalent.Thisis,ingeneral,nottrueforothercrystalsystems.Forexample,forcrystalsoftetragonalsymmetry,100and010directionsareequivalent,whereas100and001arenot.HEXA
91、GONAL CRYSTALS 六方晶体用3坐标系表示具有六方对称性的晶体时发现在某些同方向的晶向上并不具有相同的晶向指数。这种情况需要用到4坐标系，即如图3.21所示的密勒-布拉维坐标系。头3个指数代表在同一平面上（称作基准平面）的a1,a2,a3三个轴，轴与轴之间夹角互成120o。z轴垂直于该基准平面。以上介绍的晶向指数在这里用四个指数，即uvtw表示；习惯上，头3个指数代表在基准平面上的a1,a2,a3三个轴上的值，3坐标系向4坐标系转换的公式见3.7a-3.7d。公式中带有上标的字母为三坐标系的指数，而没有上标的字母是新的密勒-布拉维四坐标系的值；n是把u,v,t,w转换成最小整数的系数
92、。例如，采用这种转换，010方向就变为20。图3.22a画出了六方单位晶胞的几个不同晶向。3.13 CRYSTALLOGRAPHIC PLANESTheorientations定位ofplanesforacrystalstructurearerepresentedinasimilarmanner.Again,theunitcellisthebasis,withthethree-axiscoordinatesystemasrepresentedinFigure3.19.Inallbutthehexagonalcrystalsystem,crystallographicplanesarespeci
93、fiedbythreeMiller indices as(hkl).Anytwoplanesparalleltoeachotherareequivalentandhaveidenticalindices.Theprocedureemployedindeterminationoftheh,k,andl indexnumbersisasfollows:1. Iftheplanepassesthroughtheselectedorigin,eitheranotherparallelplanemustbeconstructedwithintheunitcellbyanappropriatetransl
94、ation,oraneworiginmustbeestablishedatthecornerofanotherunitcell.2. Atthispointthecrystallographicplaneeitherintersectsorparallelseachofthethreeaxes;thelengthoftheplanarintercept截距foreachaxisisdeterminedintermsofthelatticeparametersa,b,andc.3. Thereciprocals倒数ofthesenumbersaretaken.Aplanethatparallel
95、sanaxismaybeconsideredtohaveaninfiniteintercept,and,therefore,azeroindex.4. Ifnecessary,thesethreenumbersarechangedtothesetofsmallestintegersbymultiplicationordivisionbyacommonfactor.5. Finally,theintegerindices,notseparatedbycommas,areenclosedwithinparentheses圆括号,thus:(hkl). 关关于于晶晶向向指指数数和和晶晶面面指指数数的
96、的确确定定方方法法，还还有有以以下下两两点点说说明明：（补充内容）补充内容）1)1)参参考考坐坐标标系系通通常常都都是是右右手手坐坐标标系系? ?坐坐标标系系可可以以平平移移( (因因而而原原点点可可置置于于任任何何位位置置) )，但但不不能能转转动动，否否则则，在在不不同同坐坐标标系系下下定定出出的的指指数就无法相互比较。数就无法相互比较。2)2)如如果果晶晶面面通通过过原原点点，可可将将坐坐标标适适当当平平移移，再再求求截截距距。晶晶面面在在晶晶轴轴上上的的相相对对截截距距系系数数越越大大，则则在在晶晶面面指指数数中与该晶轴相应的指数越小；中与该晶轴相应的指数越小； 3)3)若各指数同乘以
97、异于零的数若各指数同乘以异于零的数n n，则，则晶面位向不变，晶向则或是同向晶面位向不变，晶向则或是同向( (当当n n0)0)，或是反向，或是反向( (当当n n0 0。但是，。但是，晶面距晶面距( (相邻晶面间的距离相邻晶面间的距离) )和晶向和晶向长度一般都会改变，除非长度一般都会改变，除非n n1 1。 Aninterceptonthenegativesideoftheoriginisindicatedbyabarorminussignpositionedovertheappropriateindex.Furthermore,reversingthedirectionsofallind
98、icesspecifiesanotherplaneparallelto,ontheoppositesideofandequidistant等距离from,theorigin.Severallow-indexplanesarerepresentedinFigure3.23.Oneinterestinganduniquecharacteristicofcubiccrystalsisthatplanesanddirectionshavingthesameindicesareperpendiculartooneanother;however,forothercrystalsystemsthereare
99、nosimplegeometricalrelationshipsbetweenplanesanddirectionshavingthesameindices.ATOMIC ARRANGEMENTSTheatomicarrangementforacrystallographicplane,whichisoftenofinterest,dependsonthecrystalstructure.The(110)atomicplanesforFCCandBCCcrystalstructuresarerepresentedinFigures3.24and3.25;reduced-sphereunitce
100、llsarealsoincluded.Notethattheatomicpackingisdifferentforeachcase.Thecirclesrepresentatomslyinginthecrystallographicplanesaswouldbeobtainedfromaslice切片takenthroughthecentersofthefull-sizedhardspheres.Afamilyofplanescontainsallthoseplanesthatarecrystallographicallyequivalentthatis,havingthesameatomic
101、packing;andafamilyisdesignatedbyindicesthatareenclosedinbracese.g.,100.Forexample,incubiccrystalsthe（111），（），（11），(1)，（11），(1)，(1 )and（11）planesallbelongtothe111family.Ontheotherhand,fortetragonalcrystalstructures,the100familywouldcontainonlythe(100),(100),(010),and(010)sincethe(001)and(001)planesar
102、enotcrystallographicallyequivalent.Also,inthecubicsystemonly,planeshavingthesameindices,irrespectiveoforderandsign,areequivalent.Forexample，bothand（32）belongtothe123family.HEXAGONAL CRYSTALS六方晶体对于六方对称的晶体，正如晶向那样，等价的晶面具有相同的指数，如图3.21是用密勒布拉维指数表示的。按照惯例在大多数情况下用4指数（hkil)表示，因为在六方晶体中它能够更清楚定义晶面的方向。这里多出的一个指数i可
103、以用h和k的和确定，即：i=-(h+k)其他h,k,l三个指数在立方和六方晶系指数中是等同的，图3.22b是六方晶系中的几个普通晶面。3.14 原子线密度和原子面密度3.14 LINEAR AND PLANAR ATOMIC DENSITIES在在原原子子线线密密度度的的定定义义为为：在在晶晶体体重重复复距距离离的的一一定定方方向向上上原原子子所所占占距距离离与与该该方方向向距离之比，举例距离之比，举例3.71(3.71(书书7373页）。页）。原原子子面面密密度度的的定定义义为为：单单位位晶晶胞胞晶晶体体中中穿穿过过原原子子的的任任一一平平面面，原原子子所所占占面面积积与与该平面面积之比，举
104、例该平面面积之比，举例3.72 (3.72 (书书7373页）。页）。在金属的塑性变形机理在金属的塑性变形机理-滑移（滑移（7.4节）我们将看到，线密度和面密度节）我们将看到，线密度和面密度是非常重要的。滑移发生在原子面是非常重要的。滑移发生在原子面密度最大和原子线密度最高的方向。密度最大和原子线密度最高的方向。 在晶面(hkl)中相邻两个晶面之间的垂直距离用d表示，又称面间距。当点阵常数a，b，c，,已知时，d值可用下列公式算出，即上式是用于三斜晶系的公式，用于其他晶系时可以简化，即公式中未列出菱方晶系，是因为菱方晶系可取六方晶胞，可按六方晶系公式计算；也可按菱方晶胞用三斜晶系公式简化计算。
105、问题：为什么滑移面和滑移方向往往是金属晶体中原子排列最密的晶面和晶向?答：这是因为原子密度最大的晶面其面间距最大，点阵阻力最小，因而容易沿着这些面发生滑移；滑移方向为原子密度最大的方向是由于最密排方向上的原子间距最短，即位错的伯格斯矢量b最小。3.15 CLOSE-PACKED CRYSTAL STRUCTURESMETALS It may be remembered from the discussion on metallic crystal structures (Section 3.4) that both face-centered cubic and hexagonal close
106、-packed crystal structures have atomic packing factors of 0.74, which is the most efficient packing of equalsized（等径） spheres or atoms. Inadditiontounitcellrepresentations,thesetwocrystalstructuresmaybedescribedintermsofclose-packedplanesofatoms(i.e.,planeshavingamaximumatomorsphere-packingdensity);
107、aportionofonesuchplaneisillustratedinFigure3.27a.Both crystal structures may be generated by the stacking of these close-packed planes on top of one another; the difference between the two structures lies in the stacking sequence堆积顺序.Let the centers of all the atoms in one close-packed plane be labe
108、led A. Associated with this plane are two sets of equivalent triangular depressions低洼 formed by three adjacent atoms, into which the next close-packed plane of atoms may rest. Those having the triangle vertex 高峰 pointing up are arbitrarily武断地,designated as B positions, while the remaining depression
109、s are those with the down vertices高点, which are marked C in Figure 3.27a.A second close-packed plane may be positioned with the centers of its atoms over either B or C sites; at this point both are equivalent. Suppose that the B positions are arbitrarily chosen; the stacking sequence is termed AB, w
110、hich is illustrated in Figure 3.27b. The real distinction between FCC and HCP lies in where the third close-packed layer is positioned. For HCP, the centers of this layer are aligned directly above the original A positions. This stacking sequence, ABABAB . . . , is repeated over and over. Of course,
111、 the ACACAC . . . arrangement would be equivalent. nThese close-packed planes for HCP are (0001)-type planes, and the correspondence between this and the unit cell representation is shown in Figure 3.28. For the face-centered crystal structure, the centers of the third plane are situated over the C
112、sites of the first plane (Figure 3.29a). This yields an ABCABCABC . . . stacking sequence; that is, the atomic alignment排列 repeats every third plane. It is more difficult to correlate the stacking of close-packed planes to the FCC unit cell. However, this relationship is demonstrated in Figure 3.29b
113、; these planes are of the (111) type. The significance of these FCC and HCP close-packed planes will become apparent in Chapter 8.show in crystal structure video CERAMICSA number of ceramic crystal structures may also be considered in terms of close-packed planes of ions (as opposed to atoms for met
114、als), as well as unit cells. Ordinarily, the close-packed planes are composed of the large anions阴离子. As these planes are stacked atop在顶上 each other, small interstitial sites间隙位 are created between them in which the cations阳离子 may reside.These interstitial positions exist in two different types, as
115、illustrated in Figure 3.30.Four atoms (three in one plane, and a single one in the adjacent plane) surround one type, labeled T in the figure; this is termed a tetrahedral position四面体位置, since straight lines drawn from the centers of the surrounding spheres form a four-sided tetrahedron四条边的四面体. The
116、other site type, denoted as O in Figure 3.30, involves six ion spheres, three in each of the two planes. Because an octahedron八面体 is produced by joining these six sphere centers, this site is called an octahedral position.八面体位置Thus,thecoordinationnumbersforcationsfillingtetrahedralandoctahedralposit
117、ionsare4and6,respectively.Furthermore,foreachoftheseanionspheres,oneoctahedralandtwotetrahedralpositionswillexist.Ceramiccrystalstructuresofthistypedependontwofactors:(1)thestackingoftheclose-packedanionlayers(bothFCCandHCParrangementsarepossible,whichcorrespondtoABCABC .andABABAB .sequences,respect
118、ively),and(2)themannerinwhichtheinterstitialsitesarefilledwithcations.For example, consider the rock salt crystal structure discussed above. The unit cell has cubic symmetry对称, and each cation (Na ion) has six Cl ion nearest neighbors, as may be verified from Figure 3.5. That is, the Na ion at the c
119、enter has as nearest neighbors the six Cl ions that reside at the centers of each of the cube faces. The crystal structure, having cubic symmetry, may be considered in terms of an FCC array of close-packed planes of anions, and all planes are of the 111 type.The cations reside in octahedral position
120、s because they have as nearest neighbors six anions. Furthermore, all octahedral positions are filled, since there is a single octahedral site per anion, and the ratio of anions to cations is 1 : 1. Forthiscrystalstructure,therelationshipbetweentheunitcellandclose-packedanionplanestackingschemesisil
121、lustratedinFigure3.31.Other,butnotall,ceramiccrystalstructuresmaybetreatedinasimilarmanner;includedarethezincblende闪锌矿andperovskite钙钛矿structures.Thespinel尖晶石 structure isoneoftheAmBnXp types,whichisfoundformagnesiumaluminateorspinel(MgAl2O4).Withthisstructure,theO2-ionsformanFCClattice,whereasMg2+io
122、nsfilltetrahedralsitesandAl3+resideinoctahedralpositions.Magneticceramics,orferrites,haveacrystalstructurethatisaslightvariantofthisspinelstructure;andthemagneticcharacteristicsareaffectedbytheoccupancyoftetrahedralandoctahedralpositions.面心立方、密排六方与体心立方晶胞中的间隙面心立方、密排六方与体心立方晶胞中的间隙 晶胞晶胞类型型四面体四面体间隙隙八面体八面
123、体间隙隙配配位位数数数量（与数量（与单胞中原胞中原子数之比子数之比间隙隙大小大小配配位位数数数量（与数量（与单胞中原胞中原子数之比子数之比间隙隙大小大小面心立面心立方与密方与密排六方排六方48/4=20.225R610.414R体心立体心立方方460.291R630.154RCRYSTALLINEANDNONCRYSTALLINEMATERIALS3.16SINGLECRYSTALSForacrystallinesolid,whentheperiodicandrepeatedarrangementofatomsisperfectorextendsthroughouttheentirety全部o
124、fthespecimenwithoutinterruption,theresultisasinglecrystal.All unit cells interlock in the same way and have the same orientation. Single crystals exist in nature, but they may also be produced artificially. They are ordinarily difficult to grow, because the environment must be carefully controlled.I
125、ftheextremitiesofasinglecrystalarepermittedtogrowwithoutanyexternalconstraint限制,thecrystalwillassumearegulargeometricshapehavingflatfaces,aswithsomeofthegemstones宝石;theshapeisindicativeofthecrystalstructure.AphotographofseveralsinglecrystalsisshowninFigure3.32.Within the past few years, single cryst
126、als have become extremely important in many of our modern technologies, in particular electronic microcircuits, which employ single crystals of silicon and other semiconductors.3.17 POLYCRYSTALLINE MATERIALSMostcrystallinesolidsarecomposedofacollectionofmanysmallcrystalsorgrains;suchmaterialsareterm
127、edpolycrystalline.VariousstagesinthesolidificationofapolycrystallinespecimenarerepresentedschematicallyinFigure3.33.Initially,smallcrystalsornucleiformatvariouspositions.Thesehaverandomcrystallographicorientations,asindicatedbythesquaregrids方格.Thesmallgrainsgrowbythesuccessive连续additionfromthesurrou
128、ndingliquidofatomstothestructureofeach.The extremities of adjacent grains impinge紧密接触 on one another as the solidification process approaches completion. As indicated in Figure 3.33, the crystallographic orientation varies from grain to grain. Also, there exists some atomic mismatch错配 within the reg
129、ion where two grains meet; this area, called a grain boundary晶粒界, is discussed in more detail in Section 5.8.3.18 ANISOTROPYThephysicalpropertiesofsinglecrystalsofsomesubstancesdependonthecrystallographicdirectioninwhichmeasurementsaretaken.Forexample,theelasticmodulus,theelectricalconductivity,andt
130、heindexofrefraction折射率mayhavedifferentvaluesinthe100and111directions.Thisdirectionalityofpropertiesistermedanisotropy,anditisassociatedwiththevarianceofatomicorionicspacingwithcrystallographicdirection.Substancesinwhichmeasuredpropertiesareindependentofthedirectionofmeasurementareisotropic.Theextent
131、andmagnitudeofanisotropiceffectsincrystallinematerialsarefunctionsofthesymmetryofthecrystalstructure;thedegreeofanisotropyincreaseswithdecreasingstructuralsymmetrytriclinicstructuresnormallyarehighlyanisotropic.Themodulusofelasticityvaluesat100,110,and111orientationsforseveralmaterialsarepresentedin
132、Table3.7.Formanypolycrystallinematerials,thecrystallographicorientationsoftheindividualgrainsaretotallyrandom.Underthesecircumstances,eventhougheachgrainmaybeanisotropic,aspecimencomposedofthegrainaggregatebehavesisotropically.Also,themagnitudeofameasuredpropertyrepresentssomeaverageofthedirectional
133、values.Sometimesthegrainsinpolycrystallinematerialshaveapreferential优先crystallographicorientation,inwhichcasethematerialissaidtohaveatexture.织构3.19 X-RAY DIFFRACTION: DETERMINATION OF CRYSTAL STRUCTURESx-射线衍射是用于晶体结构测定的最常规射线衍射是用于晶体结构测定的最常规和标准的方法。一束和标准的方法。一束x-射线投射到晶体表射线投射到晶体表面时，按照布拉格定律，当与一系列平行面时，按照布拉格
134、定律，当与一系列平行的原子面作用时就会发生衍射现象，衍射的原子面作用时就会发生衍射现象，衍射图谱与晶体结构、晶格常数有关，不同的图谱与晶体结构、晶格常数有关，不同的晶体有不同的衍射图谱，人们可以利用标晶体有不同的衍射图谱，人们可以利用标准物质的衍射图谱对未知物进行定性分析。准物质的衍射图谱对未知物进行定性分析。目前这些过程是通过计算机完成的。目前这些过程是通过计算机完成的。X射线和可见光相同，是一种电磁波，显示波粒二象性，但波长较可见光更短一些。X射线的波长范围为0.00110nm。(最常用的是CuK=0.1542nm)。当一束单色X射线入射到晶体时，由于晶体是由原子有规律排列成的晶胞所组成，
135、而这些有规律排列的原子间的距离与入射X射线波长具有相同数量级。故由不同原子衍射的X射线相互干涉叠加，可在某些特殊的方向上，产生强的X射线衍射。衍射方向与晶胞的形状与大小有关。衍射强度则与原子在晶胞中排列方式有关。衍射线空间方位与晶体结构的关系可用布拉格方程表示：2dsin=n式中，d为晶面间距；n为整数，称为衍射级数；为衍射半角；为X射线波长。只有在d满足上述关系时，反射束同相，干涉相互加强。可见一定的格子面对一定波长的X射线只有在一定角度时才会产生相互加强的反射。原子和分子的有规则排列可形成一定的晶体，晶体的结构有7种(见表2-1)。不同的晶系有不同的对称性，例如点对称、面对称、反轴等。为了
136、表示空间点阵面，引入了米勒(Miller)指数。每一个空间点阵面，用给定的3个米勒指数来表示。目前，衍射仪法是多晶X射线衍射中最常用、最简单的一种方法。衍射仪由X射线发生器、X射线测角仪、辐射探测器和辐射探测电路4个基本部分组成，是以特征X射线照射多晶体样品，并以辐射探测器记录衍射信息的衍射实验装置。现代X射线衍射仪还配有控制操作和运行软件的计算机系统。衍射仪法以其方便、快捷、准确和可以自动进行数据处理等特点在许多领域中取代了照相法，现在已成为晶体结构分析等工作的主要方法。晶体的x射线衍射图像实质上是晶体微观结构的一种精细复杂的变换，每种晶体的结构与其X射线衍射图之间都有着一一对应的关系，其特
137、征X射线衍射图谱不会因为他种物质混聚在一起而产生变化，这就是X射线衍射物相分析方法的依据。制备各种标准单相物质的衍射花样并使之规范化，将待分析物质的衍射花样与之对照，从而确定物质的组成相，就成为物相定性分析的基本方法。鉴定出各个相后，根据各相花样的强度正比于该组分存在的量(需要做吸收校正者除外)，就可对各种组分进行定量分析。目前常用衍射仪法得到衍射图谱，用粉末衍射标准联合会(JCPDs)编写的粉末衍射卡片(PDF卡片)进行物相分析。LiFePO4及全脱锂相FePO4的XRD图谱3.20 NONCRYSTALLINE SOLIDSIthasbeenmentionedthatnoncrystall
138、inesolidslackasystematicandregulararrangementofatomsoverrelativelylargeatomicdistances.Sometimessuchmaterialsarealsocalledamorphous(meaningliterally文字上withoutform),orsupercooledliquids,inasmuchastheiratomicstructureresemblesthatofaliquid.Anamorphousconditionmaybeillustratedbycomparisonofthecrystalli
139、neandnoncrystallinestructuresoftheceramiccompoundsilicondioxide(SiO2),whichmayexistinbothstates.Figures3.38a and3.38b presenttwo-dimensionalschematicdiagramsforbothstructuresofSiO2,inwhichtheSiO44-tetrahedronisthebasicunit(Figure3.10).Eventhougheachsiliconionbondstofouroxygenionsforbothstates,beyond
140、this,thestructureismuchmoredisorderedandirregularforthenoncrystallinestructure.Whetheracrystallineoramorphoussolidformsdependsontheeasewithwhicharandomatomicstructureintheliquidcantransformtoanorderedstateduringsolidification.Amorphousmaterials,therefore,arecharacterizedbyatomicormolecularstructures
141、thatarerelativelycomplexandbecomeorderedonlywithsomedifficulty.Furthermore,rapidlycoolingthroughthefreezingtemperaturefavorstheformationofanoncrystallinesolid,sincelittletimeisallowedfortheorderingprocess.Metalsnormallyformcrystallinesolids;butsomeceramicmaterialsarecrystalline,whereasothers(i.e.,th
142、esilicaglasses)areamorphous.Polymersmaybecompletelynoncrystallineandsemicrystallineconsistingofvaryingdegreesofcrystallinity.Moreaboutthestructureandpropertiesoftheseamorphousmaterialsisdiscussedbelowandinsubsequentchapters.SILICAGLASSESSilicondioxide(orsilica,SiO2)inthenoncrystallinestateiscalledfu
143、sed熔融 silica, orvitreous玻璃态 silica; again,aschematicrepresentationofitsstructureisshowninFigure3.38b.Otheroxides(e.g.,B2O3andGeO2)mayalsoformglassystructures(andpolyhedraloxidestructuressimilartothoseshowninFigure3.12);thesematerials,aswellasSiO2,arenetwork formerThecommoninorganicglassesthatareused
144、forcontainers,windows,andsoonaresilicaglassestowhichhavebeenaddedotheroxidessuchasCaOandNa2O.Theseoxidesdonotformpolyhedral多面体networks.Rather,theircationsareincorporatedwithinandmodifytheSiO44-network;forthisreason,theseoxideadditivesaretermednetwork modifiers. Forexample,Figure3.39isaschematicrepre
145、sentationofthestructureofasodiumsilicateglass.Stillotheroxides,suchasTiO2andAl2O3,whilenotnetworkformers,substituteforsiliconandbecomepartofandstabilizethenetwork;thesearecalledintermediates. Fromapracticalperspective,theadditionofthesemodifiersandintermediateslowersthemeltingpointandviscosity粘度ofag
146、lass,andmakesiteasiertoformatlowertemperatures.SUMMARYAtomsincrystallinesolidsarepositionedinanorderlyandrepeatedpatternthatisincontrasttotherandomanddisorderedatomicdistributionfoundinnoncrystallineoramorphousmaterials.Atomsmayberepresentedassolidspheres,and,forcrystallinesolids,crystalstructureisj
147、ustthespatialarrangementofthesespheres.Thevariouscrystalstructuresarespecifiedintermsofparallelepipedunitcells,whicharecharacterizedbygeometryandatompositionswithin.Mostcommonmetalsexistinatleastoneofthreerelativelysimplecrystalstructures:face-centeredcubic(FCC),body-centeredcubic(BCC),andhexagonalc
148、lose-packed(HCP).Twofeaturesofacrystalstructurearecoordinationnumber(ornumberofnearest-neighboratoms)andatomicpackingfactor(thefractionofsolidspherevolumeintheunitcell).CoordinationnumberandatomicpackingfactorarethesameforbothFCCandHCPcrystalstructures.Forceramicsbothcrystallineandnoncrystallinestat
149、esarepossible.Thecrystalstructuresofthosematerialsforwhichtheatomicbondingispredominantlyionicaredeterminedbythechargemagnitudeandtheradiusofeachkindofion.Someofthesimplercrystalstructuresaredescribedintermsofunitcells;severalofthesewerediscussed(rocksalt,cesiumchloride,zincblende,diamondcubic,graph
150、ite,fluorite,perovskite,andspinelstructures).Theoreticaldensitiesofmetallicandcrystallineceramicmaterialsmaybecomputedfromunitcellandatomicweightdata.Generationofface-centeredcubicandhexagonalclose-packedcrystalstructuresispossiblebythestackingofclose-packedplanesofatoms.Forsomeceramiccrystalstructu
151、res,cationsfitintointerstitialpositionsthatexistbetweentwoadjacentclosepackedplanesofanions.Forthesilicates,structureismoreconvenientlyrepresentedbymeansofinterconnectingSiO44-tetrahedra.Relativelycomplexstructuresmayresultwhenothercations(e.g.,Ca2+,Mg2+,Al3+)andanions(e.g.,OH-)areadded.Thestructure
152、sofsilica(SiO2),silicaglass,andseveralofthesimpleandlayeredsilicateswerepresented.Structuresforthevariousformsofcarbondiamond,graphite,andthefullereneswerealsodiscussed.Crystallographicplanesanddirectionsarespecifiedintermsofanindexingscheme.Thebasisforthedeterminationofeachindexisacoordinateaxissys
153、temdefinedbytheunitcellfortheparticularcrystalstructure.Directionalindicesarecomputedintermsofvectorprojectionsoneachofthecoordinateaxes,whereasplanarindicesaredeterminedfromthereciprocalsofaxialintercepts.Forhexagonalunitcells,afour-indexschemeforbothdirectionsandplanesisfoundtobemoreconvenient.Cry
154、stallographicdirectionalandplanarequivalenciesarerelatedtoatomiclinearandplanardensities,respectively.Theatomicpacking(i.e.,planardensity)ofspheresinacrystallographicplanedependsontheindicesoftheplaneaswellasthecrystalstructure.Foragivencrystalstructure,planeshavingidenticalatomicpackingyetdifferent
155、Millerindicesbelongtothesamefamily.Other concepts introduced in this chapter were: crystal system (a classification scheme for crystal structures on the basis of unit cell geometry); polymorphism (or allotropy) (when a specific material can have more than one crystal structure); and anisotropy (the
156、directionality dependence of properties).Single crystals are materials in which the atomic order extends uninterrupted over the entirety of the specimen; under some circumstances, they may have flat faces and regular geometric shapes. The vast majority of crystalline solids, however, are polycrystal
157、line, being composed of many small crystals or grains having different crystallographic orientations.3.1Whatisthedifferencebetweenatomicstructureandcrystalstructure?3.2Whatisthedifferencebetweenacrystalstructureandacrystalsystem?3.25Foraceramiccompound,whatarethetwocharacteristicsofthecomponentionst
158、hatdeterminethecrystalstructure?3.21 Thisisaunitcellforahypotheticalmetal:(a) Towhichcrystalsystemdoesthisunitcellbelong?(b) Whatwouldthiscrystalstructurebecalled?3.46 Intermsofbonding,explainwhysilicatematerialshaverelativelylowdensities.3.77 Explainwhythepropertiesofpolycrystallinematerialsaremost
159、oftenisotropic.3.51 Withinacubicunitcell,sketchthefollowingdirections:3.62 Sketch the atomic packing of (a) the (100) plane for the FCC crystal structure, and (b) the (111) plane for the BCC crystal structure (similar to Figures 3.24b and 3.25b).3.64Considerthereduced-sphereunitcellshowninProblem3.2
160、1,havinganoriginofthecoordinatesystempositionedattheatomlabeledwithanO.Forthefollowingsetsofplanes,determinewhichareequivalent:3.65 Citetheindicesofthedirectionthatresultsfromtheintersectionofeachofthefollowingpairofplaneswithinacubiccrystal:(a) (110)and(111)planes;(b) (110)and(10)planes;and(c) (10)
161、and(001)planes.3.66 Thezincblendecrystalstructureisonethatmaybegeneratedfromclose-packedplanesofanions.(a) WillthestackingsequenceforthisstructurebeFCCorHCP?Why?(b) Willcationsfilltetrahedraloroctahedralpositions?Why?(c) Whatfractionofthepositionswillbeoccupied?3.75 Hereareshowntheatomicpackingschemesforseveraldifferentcrystallographicdirectionsforsomehypotheticalmetal.Foreachdirectionthecirclesrepresentonlythoseatomscontainedwithinaunitcell,whichcirclesarereducedfromtheiractualsize.(a) Towhatcrystalsystemdoestheunitcellbelong?(b) Whatwouldthiscrystalstructurebecalled?
