1 Overview of Crystal/Defect Structure and Mechanical Properties and Behavior 1.1 INTRODUCTION The mechanical behavior of materials describes the response of materials to mechanical loads or deformation. The response can be understood in terms of the basic effects of mechanical loads on defects or atomic motion. A simple understanding of atomic and defect structure is, therefore, an essen- tial prerequisite to the development of a fundamental understanding of the mechanical behavior of materials. A brief introduction to the structure of materials will be presented in this chapter. The treatment is intended to serve as an introduction to those with a limited prior background in the principles of materials science. The better prepared reader may, therefore, choose to skim this chapter. 1.2 ATOMIC STRUCTURE In ancient Greece, Democritus postulated that atoms are the building blocks from which all materials are made. This was generally accepted by philoso- phers and scientists (without proof) for centuries. However, although the small size of the atoms was such that they could not be viewed directly with the available instruments, Avogadro in the 16th century was able to deter- mine that one mole of an element consists of 6:02  10 23 atoms. The peri- Copyright © 2003 Marcel Dekker, Inc. odictableofelementswasalsodevelopedinthe19thcenturybeforethe imagingofcrystalstructurewasmadepossibleafterthedevelopmentofx- raytechniqueslaterthatcentury.Forthefirsttime,scientistswereableto viewtheeffectsofatomsthathadbeenpostulatedbytheancients. Aclearpictureofatomicstructuresoonemergedasanumberof dedicatedscientistsstudiedtheatomicstructureofdifferenttypesofmateri- als.First,itbecameapparentthat,inmanymaterials,theatomscanbe groupedintounitcellsorbuildingblocksthataresomewhatakintothe piecesinaLegoset.Thesebuildingblocksareoftencalledcrystals. However,therearemanymaterialsinwhichnocleargroupingofatoms intounitcellsorcrystalscanbeidentified.Atomsinsuchamorphousmate- rialsareapparentlyrandomlydistributed,anditisdifficulttodiscernclear groupsofatomsinsuchmaterials.Nevertheless,inamorphousandcrystal- linematerials,mechanicalbehaviorcanonlybeunderstoodifweappreciate thefactthattheatomswithinasolidareheldtogetherbyforcesthatare oftenreferredtoaschemicalbonds.Thesewillbedescribedinthenext section. 1.3CHEMICALBONDS Twodistincttypesofchemicalbondsareknowntoexist.Strongbondsare oftendescribedasprimarybonds,andweakerbondsaregenerallydescribed assecondarybonds.However,bothtypesofbondsareimportant,andthey oftenoccurtogetherinsolids.Itisparticularlyimportanttonotethatthe weakersecondarybondsmaycontrolthemechanicalbehaviorofsome materials,evenwhenmuchstrongerprimarybondsarepresent.Agood exampleisthecaseofgraphite(carbon)whichconsistsofstrongprimary bondsandweakersecondarybonds(Fig.1.1).Therelativelylowstrengthof graphitecanbeattributedtothelowshearstressrequiredtoinducethe slidingofstrongly(primary)bondedcarbonlayersovereachother.Such slidingiseasybecausethebondsbetweenthesliding(primarybonded) carbonplanesareweaksecondarybonds. 1.3.1PrimaryBonds Primarybondsmaybeionic,covalent,ormetallicincharacter.Sincethese arerelativelystrongbonds,primarybondsgenerallygiverisetostiffsolids. Thedifferenttypesofprimarybondsaredescribedindetailbelow. 1.3.1.1IonicBonding Ionic bonds occur as a result of strong electrostatic Coulomb attractive forces between positively and negatively charged ions. The ions may be Copyright © 2003 Marcel Dekker, Inc. formed by the donation of electrons by a cation to an anion (Fig. 1.2). Note that both ions achieve more stable electronic structures (complete outer shells) by the donation or acceptance of electrons. The resulting attractive force between the ions is given by: F ¼À Q 1 Q 2 r 2 ð1:1Þ FIGURE 1.1 Schematic of the layered structure of graphite. (Adapted from Kingery et al., 1976. Reprinted with permission from John Wiley and Sons.) FIGURE 1.2 Schematic of an ionic bond—in this case between a sodium atom and a chlorine atom to form sodium chloride. (Adapted from Ashby and Jones, 1994. Reprinted with permission from Pergamon Press.) Copyright © 2003 Marcel Dekker, Inc. whereaisaproportionalityconstant,whichisequalto1=ð4" 0 )," 0 isthe permitivityofthevacuum(8:5Â10 À12 F/m),Q 1 andQ 2 aretherespective chargesofions1and2,andristheionicseparation,asshowninFig.1.2. Typicalionicbondstrengthsarebetween40and200kcal/mol.Also,dueto theirrelativelyhighbondstrengths,ionicallybondedmaterialshavehigh meltingpointssinceagreaterlevelofthermalagitationisneededtoshear theionsfromtheionicallybondedstructures.Theionicbondsarealso nonsaturatingandnondirectional.Suchbondsarerelativelydifficultto breakduringslipprocessesthataftercontrolplasticbehavior(irreversible deformation).Ionicallybondedsolidsare,therefore,relativelybrittlesince theycanonlyundergolimitedplasticity.Examplesofionicallybonded solidsincludesodiumchlorideandotheralkalihalides,metaloxides,and hydratedcarbonates. 1.3.1.2CovalentBonds Anothertypeofprimarybondisthecovalentbond.Covalentbondsare oftenfoundbetweenatomswithnearlycompleteoutershells.Theatoms typicallyachieveamorestableelectronicstructure(lowerenergystate)by sharingelectronsinoutershellstoformstructureswithcompletelyfilled outershells[(Fig.1.3(a)].Theresultingbondstrengthsarebetween30and 300kcal/mol.Awiderrangeofbondstrengthsis,therefore,associatedwith covalentbondingwhichmayresultinmolecular,linearorthree-dimensional structures. One-dimensionallinearcovalentbondsareformedbythesharingof twoouterelectrons(onefromeachatom).Theseresultintheformationof molecular structures such as Cl 2, which is shown schematically in Figs 1.3b and 1.3c. Long, linear, covalently bonded chains, may form between quad- rivalentcarbonatoms,asinpolyethylene[Figs1.4(a)].Branchesmayalso form by the attachment of other chains to the linear chain structures, as shown in Fig. 1.4(b). Furthermore, three-dimensional covalent bonded FIGURE 1.3 The covalent bond in a molecule of chlorine (Cl 2 ) gas: (a) planetary model; (b) electron dot schematic; (c) ‘‘bond-line’’ schematic. (Adapted from Shackleford, 1996. Reprinted with permission from Prentice-Hall.) Copyright © 2003 Marcel Dekker, Inc. structures may form, as in the case of diamond [Fig. 1.4(c)] and the recently discovered buckeyball structure [Fig. 1.4(d)]. Due to electron sharing, covalent bonds are directional in character. Elasticity in polymers is associated with the stretching and rotation of bonds. The chain structures may also uncurl during loading, which generally gives rise to elastic deformation. In the case of elastomers and rubber-like materials, the nonlinear elastic strains may be in excess of 100%. The elastic moduli also increase with increasing temperature due to changes in entropy that occur on bond stretching. FIGURE 1.4 Typical covalently bonded structures: (a) three-dimensional structure of diamond; (b) chain structure of polyethylene; (c) three- dimensional structure of diamond; (d) buckeyball structure of C 60 . (Adapted from Shackleford, 1996. Reprinted with permission from Prentice-Hall.) Copyright © 2003 Marcel Dekker, Inc. Plasticityincovalentlybondedmaterialsisassociatedwiththesliding ofchainsconsistingofcovalentlybondedatoms(suchasthoseinpolymers) orcovalentlybondedlayers(suchasthoseingraphite)overeachother[Figs 1.1and1.4(a)].Plasticdeformationofthree-dimensionalcovalentlybonded structures[Figs1.4(c)and1.4(d)]isalsodifficultbecauseoftheinherent resistanceofsuchstructurestodeformation.Furthermore,chainslidingis restrictedinbranchedstructures[Fig.1.4(b)]sincethebranchestendto restrictchainmotion. 1.3.1.3MetallicBonds Metallicbondsarethethirdtypeofprimarybond.Thetheorybehind metallicbondingisoftendescribedastheDru ¨ de–Lorenztheory.Metallic bondscanbeunderstoodastheoveralleffectofmultipleelectrostaticattrac- tionsbetweenpositivelychargedmetallicionsanda‘‘sea’’or‘‘gas’’of delocalizedelectrons(electroncloud)thatsurroundthepositivelycharged ions(Fig.1.5).ThisisillustratedschematicallyinFig.1.5.Notethatthe outerelectronsinametalaredelocalized,i.e.,theyarefreetomovewithin themetalliclattice.Suchelectronmovementcanbeacceleratedbytheappli- cationofanelectricfieldoratemperaturefield.Theelectrostaticforces betweenthepositivelychargedionsandtheseaofelectronsareverystrong. Thesestrongelectrostaticforcesgiverisetothehighstrengthsofmetallically bondedmaterials. Metallicbondsarenonsaturatingandnondirectionalincharacter. Hence,linedefectswithinmetallicallybondedlatticescanmoveatrelatively lowstresses(belowthoserequiredtocauseatomicseparation)byslippro- cessesatrelativelylowstresslevels.Themechanismsofslipwillbediscussed later. These give rise to the ductility of metals, which is an important prop- erty for machining and fabrication processes. FIGURE 1.5 Schematic of metallic bonding. (Adapted from Ashby and Jones, 1994. Reprinted with permission from Pergamon Press.) Copyright © 2003 Marcel Dekker, Inc. 1.3.2 Secondary Bonds Unlike primary bonds, secondary bonds (temporary dipoles and Van der Waals’ forces) are relatively weak bonds that are found in several materials. Secondary bonds occur due to so-called dipole attractions that may be temporary or permanent in nature. 1.3.2.1 Temporary Dipoles As the electrons between two initially uncharged bonded atoms orbit their nuclei, it is unlikely that the shared electrons will be exactly equidistant from the two nuclei at any given moment. Hence, small electrostatic attractions may develop between the atoms with slightly higher electron densities and the atoms with slightly lower electron densities [Fig. 1.6(a)]. The slight perturbations in the electrostatic charges on the atoms are often referred to as temporary dipole attractions or Van der Waals’ forces [Fig. 1.6(a)]. However, spherical charge symmetry must be maintained over a period of time, although asymmetric charge distributions may occur at particular moments in time. It is also clear that a certain statistical number of these attractions must occur over a given period. Temporary dipole attractions result in typical bond strengths of $ 0:24 kcal/mol. They are, therefore, much weaker than primary bonds. FIGURE 1.6 Schematics of secondary bonds: (a) temporary dipoles/Van der Waals’ forces; (b) hydrogen bonds in between water molecules. (Adapted from Ashby and Jones, 1994. Reprinted with permission from Pergamon Press.) Copyright © 2003 Marcel Dekker, Inc. Nevertheless,theymaybeimportantindeterminingtheactualphysical statesofmaterials.VanderWaals’forcesarefoundbetweencovalently bondednitrogen(N 2 )molecules.TheywerefirstproposedbyVander Waalstoexplainthedeviationsofrealgasesfromtheidealgaslaw.They arealsopartlyresponsibleforthecondensationandsolidificationofmole- cularmaterials. 1.3.2.2HydrogenBonds Hydrogenbondsareinducedasaresultofpermanentdipoleforces.Dueto thehighelectronegativity(powertoattractelectrons)oftheoxygenatom, thesharedelectronsinthewater(H 2 O)moleculearemorestronglyattracted totheoxygenatomthantothehydrogenatoms.Thehydrogenatomthere- forebecomesslightlypositivelycharged(positivedipole),whiletheoxygen atomacquiresaslightnegativecharge(negativedipole).Permanentdipole attractions,therefore,developbetweentheoxygenandhydrogenatoms, givingrisetobridgingbonds,asshowninFig.1.6(b).Suchhydrogen bondsarerelativelyweak(0.04–0.40kcal/mol).Nevertheless,theyare requiredtokeepwaterintheliquidstateatroom-temperature.Theyalso providetheadditionalbindingthatisneededtokeepseveralpolymersinthe crystallinestateatroomtemperature. 1.4STRUCTUREOFSOLIDS Thebondedatomsinasolidtypicallyremainintheirlowestenergyconfig- urations.Inseveralsolids,however,noshort-orlong-rangeorderis observed.Suchmaterialsareoftendescribedasamorphoussolids. Amorphousmaterialsmaybemetals,ceramics,orpolymers.Manyare metastable,i.e.,theymightevolveintomoreorderedstructuresonsub- sequentthermalexposure.However,therateofstructuralevolutionmay beveryslowduetoslowkinetics. 1.4.1Polymers Thebuildingblocksofpolymersarecalledmers[Figs1.7(a)and1.7(b)]. These are organic molecules, each with hydrogen atoms and other elements clustered around one or two carbon atoms. Polymers are covalently bonded chain structures that consist of hundreds of mers that are linked together via addition or condensation chemical reactions (usually at high temperatures and pressures). Most polymeric structures are based on mers with covalently bonded carbon–carbon (C – C) bonds. Single (C – C), double (C – – C), and triple (C – – – C) bonds are found in polymeric structures. Typical chains con- tain between 100 and 1000 mers per chain. Also, most of the basic properties Copyright © 2003 Marcel Dekker, Inc. of polymers improve with increasing average number of mers per chain. Polymer chains may also be cross-linked by sulfur atoms (Fig. 1.7(b)]. Such cross-linking by sulfur atoms occurs by a process known as vulcaniza- tion, which is carried out at high temperatures and pressures. Commercial rubber (isoprene) is made from such a process. The spatial configurations of the polymer chains are strongly influ- enced by the tetrahedral structure of the carbon atom [Fig. 1.7(c)]. In the case of single C – C bonds, an angle of 109.58 is subtended between the FIGURE 1.7 Examples of polymeric structures: (a) polymerization to form poly(vinyl chloride) (C 2 H 3 Cl) n ; (b) cross-linked structure of polyisoprene; (c) bond angle of 109.58; (d) bond stretching and rotation within kinked and coiled structure. (Adapted from Shackleford, 1996. Reprinted with permission from Prentice-Hall). Copyright © 2003 Marcel Dekker, Inc. carbonatomandeachofthefourbondsinthetetrahedralstructure.The resultingchainstructureswill,therefore,tendtohavekinkedandcoiled structures,asshowninFigs1.7(d).Thebondsintetrahedralstructure mayalsorotate,asshowninFig.1.7(d). Mostpolymericstructuresareamorphous,i.e.,thereisnoapparent long-orshort-rangeordertothespatialarrangementofthepolymerchains. However,evidenceofshort-andlong-rangeorderhasbeenobservedin somepolymers.Suchcrystallinityinpolymersisdueprimarilytothe formationofchainfolds,asshowninFig.1.8.Chainfoldsareobserved typicallyinlinearpolymers(thermoplastics)sincesuchlinearstructuresare amenabletofoldingofchains.Morerigidthree-dimensionalthermoset structuresareverydifficulttofoldintocrystallites.Hence,polymercrystal- linityistypicallynotobservedinthermosetstructures.Also,polymerchains withlargesidegroupsaredifficulttobendintofoldedcrystallinechains. Ingeneral,thedeformationofpolymersiselastic(fullyreversible) whenitisassociatedwithunkinking,uncoilingorrotationofbonds [Fig.1.7(d)].However,polymerchainsmayslideovereachotherwhen theappliedstressortemperaturearesufficientlylarge.Suchslidingmay berestrictedbylargesidegroups[Fig.1.4(b)]orcross-links[Fig.1.7(b)]. Permanent, plastic, or viscous deformation of polymers is, thus, associated with chain sliding, especially in linear (thermoplastic) polymers. As discussed FIGURE 1.8 Schematic of amorphous and crystalline regions within long- chain polymeric structure. (Adapted from Ashby and Jones, 1994. Reprinted with permission from Pergamon Press.) Copyright © 2003 Marcel Dekker, Inc. [...]... strong grasp of the basic concepts McClintock, F A and Argon, A.S (1993) Mechanical Behavior of Material Tech Books, Fairfax, VA This classical text provides a more advanced treatment of the fundamentals of the mechanical behavior of materials The text provides a rigorous review of the fundamental mechanics aspects of the mechanical behavior of materials Shackleford, J F (1996) Introduction to Materials. .. structural materials The mechanical properties of semiconductor devices has thus emerged as one of the fastest growing areas in the field of mechanical behavior Copyright © 20 03 Marcel Dekker, Inc FIGURE 1.13 Microstructures of some metallic and intermetallic materials: (a) grains of single phase  niobium metal; (b) duplex  þ microstructure of Ti–6Al–4V alloy; (c) eutectoid  þ microstructure of gamma-based... can affect the mechanical behavior of materials and of the role mechanics plays even on the atomic scale Failure to recognize the potential importance of these issues can lead to bad design In the worst cases, failure to understand the effects of microscale constituents on the mechanical properties of materials has led to plane crashes, bridge failures, and shipwrecks An understanding of mechanical behavior... understanding of mechanical behavior at the different scales However, since the mechanical behavior of materials is strongly affected by structure and defects, a brief review of defect structures and microstructures is provided in Chap 2 along with the indicial notation required for the description of atomic structure Copyright © 20 03 Marcel Dekker, Inc FIGURE 1.16 Examples of composite microstructures (a) Al2O3... Al2O3 particulatereinforced Al composite (Courtesy of Prof T S Srivatsan.) (b) TiB whiskerreinforced Ti–6Al–4V composite (c) SiC fiber-reinforced Ti–15V–3Cr–3Al–3Sn composite (d) Layered MoSi2/Nb composite 1.6 SUMMARY A brief introduction to the structure of materials has been presented in this chapter Following a review of the structure of crystalline and amorphous materials, the different classes of materials. .. predict the mechanical properties of composites The fracture behavior but not the stiffness of most composites are also strongly affected by the interfacial properties between the matrix and reinforcement phases The interfaces, along with the matrix, must be engineered carefully to obtain the desired balance of mechanical properties FIGURE 1.15 Schematic of typical semiconductor package (Courtesy of Dr Rheiner... structures also exist in all of the electronic packages that are used in modern electronic devices Since the reliability of these packages is often determined by the thermal and mechanical properties of the individual layers and their interfaces, a good understanding of composite concepts is required for the design of such packages Electronic packages typically consist of silica (semiconductor) layers... Copyright © 20 03 Marcel Dekker, Inc metallic substrates within polymeric composites (usually silica filled epoxies) The other materials that have been used in electronic packaging include: alumina, aluminum, silicon nitride, and a wide range of other materials The layered materials have been selected due to their combinations of heat conductivity (required for Joule/I2 R heat dissipation) and electrical properties. .. (Courtesy of Dr Rheiner Dauskardt.) Copyright © 20 03 Marcel Dekker, Inc An almost infinite spectrum of composite materials should be readily apparent to the reader However, with the exception of natural composites, only a limited range of composite materials have been produced for commercial purposes These include: composites reinforced with brittle or ductile particles, whiskers, fibers, and layers [Figs... the reinforcement phase Composites constitute the great majority of materials that are encountered in nature However, they may also be synthetic mixtures In any case, they will tend to have mechanical properties that are intermediate between those of the matrix and Copyright © 20 03 Marcel Dekker, Inc FIGURE 1.14 Schematic illustration of semiconduction via: (a) electron movement; (b) hole movement . 1 Overview of Crystal/Defect Structure and Mechanical Properties and Behavior 1.1 INTRODUCTION The mechanical behavior of materials describes the response of materials to mechanical loads. macroscopic level of understanding of structure [Figs 16(a)–(d)]. They are often unaware of the atomic and micro- structural constituents that can affect the mechanical behavior of materials and of the. Inc. Nevertheless,theymaybeimportantindeterminingtheactualphysical statesofmaterials.VanderWaals’forcesarefoundbetweencovalently bondednitrogen(N 2 )molecules.TheywerefirstproposedbyVander Waalstoexplainthedeviationsofrealgasesfromtheidealgaslaw.They arealsopartlyresponsibleforthecondensationandsolidificationofmole- cularmaterials. 1.3 .2. 2HydrogenBonds Hydrogenbondsareinducedasaresultofpermanentdipoleforces.Dueto thehighelectronegativity(powertoattractelectrons)oftheoxygenatom, thesharedelectronsinthewater(H 2 O)moleculearemorestronglyattracted totheoxygenatomthantothehydrogenatoms.Thehydrogenatomthere- forebecomesslightlypositivelycharged(positivedipole),whiletheoxygen atomacquiresaslightnegativecharge(negativedipole).Permanentdipole attractions,therefore,developbetweentheoxygenandhydrogenatoms, givingrisetobridgingbonds,asshowninFig.1.6(b).Suchhydrogen bondsarerelativelyweak(0.04–0.40kcal/mol).Nevertheless,theyare requiredtokeepwaterintheliquidstateatroom-temperature.Theyalso providetheadditionalbindingthatisneededtokeepseveralpolymersinthe crystallinestateatroomtemperature. 1.4STRUCTUREOFSOLIDS Thebondedatomsinasolidtypicallyremainintheirlowestenergyconfig- urations.Inseveralsolids,however,noshort-orlong-rangeorderis observed.Suchmaterialsareoftendescribedasamorphoussolids. Amorphousmaterialsmaybemetals,ceramics,orpolymers.Manyare metastable,i.e.,theymightevolveintomoreorderedstructuresonsub- sequentthermalexposure.However,therateofstructuralevolutionmay beveryslowduetoslowkinetics. 1.4.1Polymers Thebuildingblocksofpolymersarecalledmers[Figs1.7(a)and1.7(b)]. These