研一-材料结构

DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresChapter1The

StructureofMaterials:OverviewDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresHowtostudymaterials?Fouraspectsofmaterialresearch:Structure,properties,processing,performanceDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTheMSEtetrahedronemphasizestheconnectionsbetweenthestructure,processing,propertiesandperformance,notingpleasethestructureisplacingintheprimaryposition.DifferentStructure,differentproperty.Structure:overviewDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTwodimensionalcontinuousrandomnetworkstructureinanA2B3compound.Noncrystalandcrystalhavedifferentstructuresandthusproperties.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTable1-1Comparisonofpropertiesoflowquartzandvitreoussilica.Differentstructuresleadtodifferentproperties,inspiteofthesamecompositions.MaterialDensity(g/cm3)Thermalexpansioncoefficient(10-6K-1)IndexofrefractionLowquartz(SiO2)2.651=13n1=1.553

2=8n2=1.544Vitreoussilica(SiO2)2.200.5(isotropic)1.59(isotropic)

DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTheDesignofMicrostructureTheArtificialDesignedFunctionalPropertiesDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresWhatisTheStructureofMaterials?StructureofMaterialsconcernsthequantitativedescriptionofthearrangementsofthecomponentsthatmakeupthematerialsonallrelevantlengthscales.不同尺度上、定量、组分堆砌。HowtodescribeTheStructureofMaterials?0.1mmonedgeofcubicNaClcontains1020atoms:Impossibletodescribeeveryatoms/ionsbecausethevasenumberofatomsinvolved,iftheatomsarenotideal,perfectlyordered,periodicallyarranged.Otherwise,itisdescribable.(representativeunit)Realmaterialscontainsdefects/imperfections.Structurehierarchy:lengthscale.Atom(Å)–cluster(nm)–singlegrain(m)–grainstructure(mm)–macrostructure(cm)Averagingisnecessary!DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures§1.1HistoryofMaterialsStructureResearch:1.1860s,HenryCliftonSorbyMicrostructureofpolished,etchedsteelsamples.OpticalMicroscopy2.1890s,Laue,Nobelprizein1914.X-ray,then1912,diffractionmethodwasdeveloped.X-raywasappliedtodeterminestructure.Braggs,fatherandson,Nobelprizein1915.3.1920s,1923,RamanscatteringispredicatedbyA.Smekal,etal.1928,RamanobservedthescatteringinCCl4.4.1950s,Electronmicroscopyformicrostructureandsomewhatlater,field-ionmicroscopyforpointdefect.5.1980sandlater,Scanningprobemicroscopy(STM,AFM,et.)someevencanallowreal-spaceimagebutnotreciprocalspaceimage.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures§1.2DescriptorsandAveraging:Descriptorsprovideconceptualschemethatdescriptprecisecharacterizationofsomeaspectsofstructure:Fornoncrystal:Forcrystal:Forliquidcrystal:Averaging:Vastnumberofatomsinatinymaterials.Notnecessarytoknowtheexactlocationandcircumvents.e.g.,compositionalinhomogeneitiesareidealbutnotreal,PMN-PT,BNT-BT.Needareferencestatefordescribingstructure:Crystallinestate:IdealstateNoncrystallinestate:Spatialaveraged.LiquidState:Spatialandtimeaveraged.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresReferencestatefornon-crystallinematerials:

Noidealreferencestateforcompositionwiththerealstructure.Non-crystallinematerialsdonothavecompletelyrandomstructure.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures§1.3PreliminaryConcepts:§1.3.1SymmetrySymmetry,asetofconceptsforspecificationofstructure,particularlyimportantforcrystallinebutalsousefulfordescribingtheliquidcrystallineandnon-crystallinestatesaswellasthestructureofindividualmolecules.Anobjectissaidtohavesymmetrywhenthereisexactcorrespondenceofitsconstituentpartsonoppositesidesofadividinglineorplane,oraboutacenteroranaxis.Indistinguishablebeforeandaftersymmetryoperation.Allmaterialspossesssomesymmetries.Symmetry-propertyrelationship:Neumann’Principle.Fourbasicsymmetryoperations:translation,rotation,reflectionandinversion.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTranslationalsymmetry:whenaobjectorcollectionofobjectsisrepeatedindefinitelybysuccessiverigid-bodydisplacementsspecifiedbyavectort.Thepatternwithtranslationalsymmetryshouldbeinfinite.Indistinguishable.Ifonevectorisinvolved,thusonedimensionalperiodicity,iftwo(noncollinear),twodimensionalperiodicity,andifthree,threedimensionalperiodicity.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTranslationsoft1,t2,andt3willbuildaninfiniteNiAlcrystalDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresRotationalsymmetry:WhichinvolvesrepetitionaboutasymmetryaxisA,therepeatedobjectofpatternwillsuperimposeonitselfaftern=2/rotations.nisaninteger.Amaterialwithtwofoldrotationalsymmetryaxisisshowbelow:DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresLocationofatwofoldrotationalsymmetryaxisintetragonalcrystalHgCuBa2O9,ahighTcsuperconductor.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresReflectionsymmetry:Whichcanoccuraboutalineinatwodimensionalobjectoraboutaplaneinathreedimensionalobject.In2D,(i)Itcausesanobjecttoberepeatedasitsownmirrorimageontheoppositesideofthereflectionline.(ii)Themirrorimagelocateatthesamedistancefromthereflectionlineastheoriginalobject.

(2)In3D,operatesanalogously.(3)Handednesschanged.手性:一个物体与其镜像不重合(4)Example:3D,thefollowingfigure.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresHandednesschangesacrossalineofreflectionsymmetryDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresInversionsymmetry:(1)Onlyin3D.(2)Existatapointcalledinversioncenter.(3)Whateverexistsatanarbitrarypointatapositiontfromtheinversioncentermapsontoanidenticalpointatposition–t.(4)Handednesschangedofanasymmetricobject.(5)Example,thefollowingfigure.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresEthanemoleculehasaninversioncenteratthemidpointoftheC-Cbond.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures1:Atomicstructure2:Bonding§1.3.2BondingDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures1:Atomicstructure——可看成是原子核及分布在核周围的电子组成。原子原子核——中子和质子组成，核的体积很小，集中了原子的绝大部分质量。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures电子——绕着原子核在一定的轨道上旋转,质量虽可忽略，但电子却涉及原子结构中一些重要的问题，它不仅决定单个原子的行为，也对工程材料内部原子的结合及某些性能起着决定性作用。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures电子运动的轨道：

由四个量子数决定，分别是主量子数、次量子数、磁量子数及自旋量子数。主量子数n=1,2,3…——决定电子离核远近和能量高低的主要参数。次量子数(角量子数或角动量量子数、l=0,1,2…)——量子轨道并不一定总是球形的，次量子数反映了轨道的形状，各轨道在原子核周围的角度分布不同。它也影响轨道的能级，按s、p、d、f…依次升高。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures磁量子数——确定了轨道的空间取向，以m(或ml=-l,-l+1,…l)表示。没有外磁场时，处于同一亚壳层而空间取向不同的电子具有相同的能量，但在外加磁场下，不同空间取向轨道的能量会略有所差别。自旋量子数——ms=+1/2，–1/2，表示在每个状态下可以存在自旋方向相反的两个电子。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresnlml

记号1001s2002s2102pz2112px2py3003s3103pz3113px3py

3203dz23213dxz3dyz3223dx2-y23dxy电子轨道DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures电子轨道三维形状图DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures1、正负号是波函数的正负；2、2px,2py,2pz分别沿x,y,z轴伸展。3dx2-y2沿x和y伸展；3dz2的正值沿z伸展，而在xy面成圆柱对称分布。3dxy,3dxz,3dyz则在下标标明的两个坐标轴间的平分线向外伸展。3、这告诉我们，如果电子占据某个轨道，应该怎样去寻找这个电子。如：当电子占据2pz轨道，应从+z和-z方向去寻找。*例如：2pz,3pz电子寻找方向相同（轨道形状相同），但是最可能找到的地点不同（波函数的极大值不同）。其他同理。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresd轨道在晶体场中的分裂：简单情况，考虑一个过渡金属元素离子在正八面体晶体场中的情况：6个带负电的氧离子沿x,y,z向中心阳离子接近；中心阳离子沿坐标轴方向伸展的dx2-y2和dz2的轨道与氧离子迎头相碰，这两个轨道上的电子受到排斥作用，能量增高；沿对角线方向伸展的dxy,dxz,dyz轨道正好能插入配位氧离子构成的配位体的间隙，因此，能量降低；原来能量相等的5组轨道分裂为两组：能量较高的,eg轨道，能量较低的,t2g轨道；DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresd轨道在晶体场中的分裂：晶体场分裂参数：eg和t2g轨道电子的能量之差。

0=E(eg)-E(t2g)d轨道在晶体场中的分裂，服从“重心”规则，即分裂过程中，总能量保持不变。（晶体场理论只涉及到能量相对大小，不必考虑其绝对能量是多少，因此：DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures

原子核外电子的分布与四个量子数有关，且服从下述两个基本原理：（1）泡利不相容原理一个原子中不可能存在有四个量子数完全相同的两个电子。（2）最低能量原理电子总是优先占据能量低的轨道，使系统处于最低的能量状态。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures元素周期表及性能的周期性变化原子周期律——早在1869年，俄国化学家已发现了元素性质是按原子相对质量的增加而程周期性的变化。这正是由于原子核外电子的排列是随原子序数的增加呈周期性变化。族——周期表上竖的各列。同一族元素具有相同的外壳层电子数，同一族元素具有非常相似的化学性能。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures过渡元素——周期表中部的ⅢB~ⅧB对应着内壳层电子逐渐填充的过程，把这些内壳层未填满的元素称过渡元素。

各个元素所表现的行为或性质一定会呈现同样的周期性变化，因为原子结构从根本上决定了原子间的结合键，从而影响元素的性质。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures2:bondingPropertyisstronglyinfluencedbytheinter-atomicbondsandthusbytheoutermostvalenceelectrons.Bondingbetweenatomsisextremelyvariable:e.g.,TiCl4andTiCl2AtRT,TiCl4isliquidandTiCl2iscrystallinesolid.ThereasonisthattheTi-ClbondinTiCl2isionicincharacter,ionsarearrangedinorderandheldtogetherbyCoulombicforce,whereasinTiCl4iscovalent,themolecularinteractionthroughvanderWaalsforce.Bondingiscomplicated.ByExploringthenatureoftheforcesthatholdatomstogether,fourtypesofbondscanbedistinguished:covalent,ionic,metallicandvandeWaals.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresCovalent,ionic,metallicbondsarequitestrongwhereasvanderWaalsbondisrelativeweak.

Covalentbond,theaveragebondingenergy:~5eV;Ionicbond:~1-3eV;Metallicbond:~0.5eV;VanderWaalsbond:0.001-0.1eV.Thewiderangeisduetodifferenttypesofinteractionsresponsibleforthebonds

AtRT,kBTisabout0.03eV,wherekB

isBoltzmann’sconstant.ThatiswhythesubstanceswithvanderWaalsbondsareusuallygasorliquidatRT.Athighertemperature,eventhestrongbondscanbedisruptedandsolidmelts.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTheFormationofBonding:在凝聚状态下，原子间距离十分接近，便产生了原子间的作用力，使原子结合在一起，就形成了键。Allthebondsthatfrombetweenatomsinvolvetheoutermostvalenceelectronswhichcanbegained,lost,orshared.Incontrast,weakvanderWaalsbondinvolvenochargetransfer,ratherdipolesinteractions.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresGeneralschematicofhowtheoutervalenceelectronsofatomsaredistributedInvarioustypesofbond,DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures各种键的实例DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures离子键——当两类原子(一般是金属-非金属原子)结合时，金属原子的外层电子很可能转移到非金属原子外壳层上，使两者都得到稳定的电子结构，从而降低体系的能量，此时金属原子和非金属原子分别形成正离子和负离子，正负离子间相互吸引，使原子结合在一起，这就是离子键。即离子键是正负离子间由静电力作用结合成离子化合物的化学键。*非局域作用力*无分子概念。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures共价键——价电子数较多的元素，离子化比较困难，在这种情况下，相邻原子间可以共同组成一个新的电子轨道，由两个原子中各有一个电子共用，利用共享电子对来达到稳定的电子结构。这就是共价键。*饱和性；*方向性；*分子概念：形成共价键的分子团；*轨道杂化；以碳氢化合物为例：sp3,sp2,sp,

sp3杂化：四面体轨道(CH4甲烷)sp2杂化：三角形杂化，第三个2p电子仍然在2p态，其轨道与三角形平面垂直。（C2H4乙烯）sp:C原子中2s电子与2p电子的对角杂化，杂化后新轨道为哑铃状，另两个电子仍然在2p态且轨道相互垂直，处于哑铃的中垂面内。（C2H2乙炔)DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures*键，键。1、分子轨道近似认为是原子轨道的线性组合。2、两个轨道以头碰头的方式发生轨道重叠(角动量沿键轴分量为零)，这样的轨道为轨道：能量低的为成键轨道，高的为反键轨道，成键/反键轨道上的电子为成键/反键电子，成键电子使分子稳定，反键电子式分子倾向于离解。轨道上电子的稳定性而构成的共价键，称为键。3、以肩并肩的方式发生轨道重叠(角动量沿键轴分量不为零)，这样的轨道为轨道：成键/反键轨道、电子。由成键的电子构成的共价键称为键。4、键形成时轨道重叠程度比大，所以前者键能大，后者键能小。即后者的电子活性较高。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures共价晶体特点：1、共价晶体中，无自由电子和离子，故呈现绝缘特征；2、键合能大，熔点和硬度高：金刚石熔点>3000度；3、如只有成键电子，一般为抗磁性：为磁场所排斥。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresHowtodistinguishcovalentbondsfromionicbonds?DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures原子的电离能：原子失去一个电子变为气态+1价离子所需要的能量，称为第一电离能I1+1价离子失去一个电子，变成+2价离子所需能量，第二电离能I2元素周期表：I1：碱金属最小；惰性元素最大同一种元素：I1<I2<…<InDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures原子的第一电离能与原子序数的关系：DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures原子的电子亲和能：原子获得一个电子变为气态-1价离子所放出的能量，称为电子亲和能。实验测定困难，数据可靠性差。一般随原子半径的减少而增加，因为半径小，核电荷对电子的吸引力增加。元素周期表同一族元素，由上到下的方向减小。

H(0.75)-Li(0.62)-Na(0.55)-K(0.50)-Rb(0.49)-Cs(0.47)DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures电负性：有助于判断键的行踪、键型、键的极性等。原子电负性x可用原子的第一电离能和电子亲和能之和来简单衡量：

x=I1+ERelativeelectronegativity:Whichisdefinedastherelativeabilityofanatomtodrawelectronstowarditself.Iftwobondingatomshavethesameelectronegativity,thevalenceelectronsaresharedequallyandthebondispurelycovalent.Ifthetwobondingatomshaveverydifferentelectronegativity,themoreelectronegativeatomswithdrawsnearlyallofthevalenceelectrondensityandthebondispurelyionic.AnexampleisNaCl.Ifthedifferenceinelectronegativityisintermediate,thetypeofformedbondshavebothcovalentandioniccharacters.Socalledpolarcovalentbond.Inthiscase,oneatomhasapartialpositivecharge(+)andtheotherhasapartialnegativecharge(-).AnexampleisHCl.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures原子的电负性（eV)*Pauling,ThenatureofChemicalbondDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures金属键自由电子气与离子键不同，只有正离子，负离子的作用被自由电子代替。无饱和性，方向性，因此具有配位数大和密度高等特点。存在松散电子，因此电导率、热导率高。Allatomssharetheirvalencecharges.Nucleiformapositivelychargedarray.Nowelldefinedmoleculesbecausethebondingforceislongrange.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures范德瓦耳斯键:分子-分子间存在的短程、弱相互作用力，主要来源有三种：（1）取向力：发生在极性分子间，极性分子间的作用使得分子有定向排列的趋势。与极性分子的偶极距大小相关。（2）诱导力：极性分子和非极性分子间，在极性分子偶极距电场作用下，非极性分子电子云发生变化，产生诱导极距，两种偶极距产生吸引。与极性分子的偶极距大小、非极性分子的极化率有关。（3）色散力：非极性分子，如惰性气体间。分子的瞬间偶极距相互作用的结果：瞬间电子分布不均匀，产生瞬间偶极距。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures极化分子间的作用力正电中心负电中心原子核电子云a)原子核电子云+–b)c)a)理论的电子云分布b)原子偶极矩的产生c)原子（或分子）间的范德瓦耳斯键结合DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures*氢键

氢键的本质与范德瓦耳斯键一样，只是氢原子起了关键作用。氢原子只有一个电子，当氢原子与一个电负性很强的原子X结合成分子时，氢原子的一个电子转移至该原子壳层上；分子的氢离子侧实质上是一个裸露的质子，对另个易失去电子的原子Y表现出较强的吸引力，这样，氢原子便在两个电负性很强的原子之间形成一个桥梁，把两者结合起来，形成氢键。所以氢键可表达为：

X–H——YDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures混合键只有一种键型结合而成的化合物，称为单键型化合物。例如NaCl、金刚石、金属、惰性气体分别由离子键、共价键、金属键合范氏键结合。实际材料中单一结合键并不多，大部分材料的内部原子结合键往往是各种键的混合。例如：ⅣA族的Si、Ge、Sn元素的结合是共价键与金属

键的混合。陶瓷化合物中出现离子键与共价键混合的情况。离子键和共价键混合：例如ZnS：Zn和S原子都是4配位。共价键和金属键混合：石墨：层内共价和金属混合键，

层键范氏键结合。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures结合键的本质与原子间距

固体原子中存在两种力：吸引力和排斥力。它们随原子间距的增大而减小。当距离很远时，排斥力很小，只有当原子间接近至电子轨道互相重叠时斥力才明显增大，并超过了吸引力。在某一距离下引力和斥力相等，这一距离r0相当于原子的平衡距离，称原子间距。

DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresB为常数，n为波恩指数。吸引力和排斥力相等时，能量最低，为平衡态。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures键与性能1、物理性能（1）熔点的高低代表了材料稳定性的程度。共价键、离子键化合物的熔点很高这是陶瓷材料比金属材料具有更高热稳定性的根本原因。范氏键结合的材料熔点一定偏低，如聚合物等。（2）材料的密度与结合键类型有关。金属有高的密度，聚合物密度最低。（3）金属键使金属材料具有良好的导电性和导热性，而由非金属键结合的陶瓷、聚合物均在固态下不导电。

2、力学性能

结合键是影响弹性模量的主要因素。结合键能越大，弹性模量越大，材料的强度越大。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures键的各种参数：1：键长：两个相邻核之间的距离。下表是C-C和C-Ti之间的键长MoleculeFormulaC-C(Å)EthaneCH3-CH31.54EthyleneCH2=CH21.33AcetyleneCHCH1.20BenzeneC6H61.39DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTable1-3ExamplesofTitanium-ChoorinebondlengthsCrystallineionicsolidTiCl22.38（离子键）LiquidTiCl42.18（共价键、范氏键）MaterialsStateFormulaTi-Cl(Å)DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures2：键角Bondangles:Definedastherelativelocationofthreeatoms.Example:linearCO2,trigonalplanarBF3,tetrahedralCH4,etc.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures3：键能形成键所释放的能量共价>离子>金属>范德瓦耳斯DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures4：原子和离子半径：离子半径与价态、（自旋）、配位数等密切相关；对设计新材料的性能、探索新型材料具有重要作用。Sizeofatomsandions:Thesizeofisolatedatomsisdeterminedbythedistancetheelectrondistributionextendsfromthenucleus.Actually,thisismeanless.WhenAtomsarebonded,theshapeofelectrondistributiondependsonthenumberandtypeofbonds.IonicRadii:Itdependsonthechargesoftheionsandtheirmutualarrangements.Aneutralatomispositivelyornegativelycharged,itssizedecreasesorincreases,respectively,becauseofthechargedbondingabilityoftheoutermostelectrons.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresMetallicandionicradii.ElementMetallicRadius(Å)IonicRadius(Å)(ionicvalence)Li1.520.78(+1)Na1.860.98(+1)K2.311.33(+1)Mg1.590.65(+2)Fe1.240.83(+2)Ti1.460.64(+4)Au1.441.37(+1)DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresPlotofatomicsizevs.atomicnumber.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures第一系列过度金属元素的离子半径r和d电子数n的关系（空心圆为高自旋态，实心圆为低自旋态）。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures一组6配位的离子半径（pm)ActaCrystallograA32,751(1976)[注：以O2-半径140pm,F-为133pm为参考标准值。]DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresCovalentRadii:Definedasone-halfofthecovalentbondlengthbetweenadjacentatoms.A-Abondlength,B-Bbondlength,andapproximatedA-Bbondlength.Thefollowingtableliststhecovalentradiiforcarbon,nitrogen,oxygen.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresDepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures范德瓦耳斯半径：1、分子以范德瓦耳斯力结合时，相邻分子的接触原子所表现出的半径。例如：Cl晶体，两个相邻分子的相互接触的Cl原子间距0.36nm，那么Cl原子的范德瓦耳斯半径为0.18nm，比Cl原子的共价半径（0.10nm)大，而和Cl离子半径（0.181nm)接近。2、范德瓦耳斯半径一般比同种单质原子的共价半径大。DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructures成键电子对：中心原子的电子和其他原子的电子构成共价键。孤对电子：中心原子的两个电子构成电子对，未参与形成共价键。MoleculargeometryPolyatomiccovalentlybondedmolecules:electron-domaintheoryFocusonthe3Ddistributionoftheoutermostelectronsaboutagivenatomandhowtheseelectronswillpairwithotherelectronsfrombondingatoms.Thesevalenceelectronstendtobindaspairswithoppositespin,denotedaselectrondomain.Twotypesofdomains:(i)Bondingdomain:Thepairedelectronsaresharedbetweentwobondingatoms.(ii)Nonbondingdomain:thepairofelectronsbelongstoaparticularatom.Thenonbondingelectrondomainoccupiesalargerspacethanthebondingelectrondomain.Twotendenciesofelectrondomain:(i)Arrangethemselvesascloselyaspossibletoacentralatom.(ii)Avoidotherelectrondomainsasmuchaspossible.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresMoleculeswithmultiplylinkedatomsmayhavealargesetofoverallshapesbecauseofthepossiblerotationaboutbonds:

Forsimplemolecules,electrondomaincansomewhatpredicatetheshapeofmolecules.Examplesaregivenbelow.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresThegeometryofthevalenceelectronsinsomematerials.(a)CH4(b)NH3(c)H2ODepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresSchematicofthebondinggeometryofBF3andCO2.DepartmentofMaterialsScienceandEngineeringNationalLaboratoryofSolid-StateMicrostructuresTable1-6ElectrondistributionsandmolecularshapesElectronBondingNonbondingDistributionMolecularDomainEDEDofElectronsGeometry2(sp)20LinearLinear11LinearLinear3(sp2)30TrigonalplanarTrigonalplanar21TrigonalplanarBent12TrigonalplanarLinear4(sp3)40