Chapter3StructuresofMetalsandCeramics Highvelocityelectronbeamswavelike wavelengthsshorterthaninteratomicspacings diffractionbyatomicplanesincrystallinematerials Asx rays WhyStudyStructuresofMetalsandCeramics propertiesofsomematerials crystalstructures directlyrelatedby Forexample Magnesium Mg Beryllium Be Havingsamecrystalstructure morebrittlethan Gold Au Silver Ag Havingsamecrystalstructure CrystallineandNoncrystalline Differentproperty havingthesamecompositionbutdifferentstructure 3 1INTRODUCTION Chapter2wasconcernedatomicbonding theelectronstructureoftheindividualatoms Inthischapter nextlevelofthestructureofmaterialsthearrangementsofatomsinthesolidstate Introducingtheconcepts crystalandnoncrystal Forcrystalstructure unitcell crystallographicdirectionsandplanes metalsandceramics Singlecrystalsandpolycrystalline 非晶体 晶体 晶胞 单晶体 多晶体 3 2FundamentalConcepts Crystalline Thestateofasolidmaterialcharacterizedbyaperiodicandrepeatingthree dimensionalarrayofatoms ions ormolecules long rangeorder theatomswillpositionthemselvesinarepetitivethree dimensionalpattern inwhicheachatomisbondedtoitsnearest neighboratoms Allmetals manyceramicmaterials andcertainpolymersformcrystallinestructures Materials crystalline Noncrystallineoramorphous Nolong rangeatomicorder 长程有序 Thedescriptionofcrystalline atomichardspheremodel UnitCells晶胞 3 3UnitCells hardspherelatticeunitcells 晶格 atomichardspheremodel atoms orions arethoughtofasbeingsolidsphereshavingwell defineddiameters lattice Theregulargeometricalarrangementofpointsincrystalspace meansathree dimensionalarrayofpointscoincidingwithatompositions unitcells Thebasicstructuralunitofacrystalstructure Itisgenerallydefinedintermsofatom orion positionswithinaparallelepipedorprismsvolume thelatticeparameters Thecombinationofunitcelledgelengthsandinteraxialanglesthatdefinestheunitcellgeometry a b c and 硬球模型 晶格 晶胞 晶格常数 平行六面体 棱柱 Crystalstructure Forcrystallinematerials themannerinwhichatomsorionsarearrayedinspace Itisdefinedintermsoftheunitcellgeometryandtheatompositionswithintheunitcell Aunitcellischosentorepresentthesymmetryofthecrystalstructure theunitcellisthebasicstructuralunitorbuildingblockofthecrystalstructure 对称性 3 4MetallicCrystalStructures norestrictionsastothenumberandpositionofnearest neighboratoms denseatomicpackings Threerelativelysimplecrystalstructures face centeredcubic body centeredcubic andhexagonalclose packed 1 TheFace centeredCubicCrystalStructure Acrystalstructurefoundinsomeofthecommonelementalmetals Withinthecubicunitcell atomsarelocatedatallcornerandface centeredpositions 面心立方晶格 无限制 原子密堆 FIGURE3 1Fortheface centeredcubiccrystalstructure a ahardsphereunitcellrepresentation b areduced sphereunitcell and c anaggregateofmanyatoms a b cand 90oatomslocatedateachofthecornersandthecentersofallthecubefaces theface centeredcubic FCC 1 thecubeedgelengthaandtheatomicradiusRarerelatedthrough 2 Thenumberofatominunitcell n 原子半径 晶胞原子数 3 CoordinationNumber CN Thenumberofatomicorionicnearestneighbors For FCC crystalstructure CN 12 配位数 4 AtomicPackingFactor APF Thefractionofthevolumeofaunitcellthatisoccupiedby hardsphere atomsorions 紧密系数 致密度 2 TheBody centeredCubicCrystalStructure body centeredcubic BCC a b cand 90oatomsarelocatedatcornerandcellcenterpositions FIGURE3 2Forthebody centeredcubiccrystalstructure a ahardsphereunitcellrepresentation b areduced sphereunitcell and c anaggregateofmanyatoms 体心立方晶格 1 thecubeedgelengthaandtheatomicradiusRarerelatedthrough 2 Thenumberofatominunitcell n 3 CN 8 4 3 TheHexagonalClose packedCrystalStructure hexagonalclose packed HCP Thetopandbottomfacesoftheunitcellconsistofsixatomsthatformregularhexagonsandsurroundasingleatominthecenter Anotherplanethatprovidesthreeadditionalatomstotheunitcellissituatedbetweenthetopandbottomplanes a b cc a 1 633anda b 90og 120o FIGURE3 3Forthehexagonalclose packedcrystalstructure a areduced sphereunitcelland b anaggregateofmanyatoms 密排六方晶格 2 Thenumberofatominunitcell n 3 CN 12 4 1 thecubeedgelengthaandtheatomicradiusRarerelatedthrough a c 铬 镉 钴 3 5DensityComputations metals n numberofatomsassociatedwitheachunitcellA atomicweightVc volumeoftheunitcellNA Avogadro snumber 6 023 1023atoms mol EXAMPLE Copper R 0 128nm 1 28 FCC ACu 63 5g mol Theliteraturevalueforthedensityofcopperis8 94g cm3 3 6CeramicCrystalStructures Ceramicsleasttwoelementsormore crystalstructuresmorecomplex atomicbondingfrompurelyionictototallycovalent sometimes twobondingtypes thedegreeofioniccharacterdependentontheelectronegativities ByEquation2 10andFigure2 7 Table3 2thepercentioniccharacter Table3 2ForSeveralCeramicMaterials PercentIonicCharacteroftheInteratomicBonds crystalstructuresofceramicmaterialsbondedinpredominantlyionic Cations Anions Apositivelychargedmetallicion 阳离子 阴离子 Anegativelychargednonmetallicion Twocharacteristicsofinfluencethecrystalstructure themagnitudeoftheelectricalchargeions therelativesizesofthecationsandanions thecrystalmustbeelectricallyneutral thatis allthecationpositivechargesmustbebalancedbyanequalnumberofanionnegativec