... Inc.ÆÀ1¼1=5boundaryisoneinwhich1in5ofthegrainboundaryatomsmatch,asshowninFig.2.8(c).Twinboundariesmayformwithincrystals.Suchboundarieslieacrossdeformationtwinplanes,asshowninFig.2.8(d).Notethattheatomsoneithersideofthetwinplanesaremirrorimages.Stackingfaultsmayalsobeformedwhentheperfectstackinginthecrystallinestackingsequenceisdisturbed,Figs2.8(e)and2.8(f).Thesemaybethoughtofastheabsenceofaplaneofatoms(intrinsicstackingfaults)ortheinsertionofrowsofatomsthatdisturbthearrangementofatoms(extrinsicstackingfaults).IntrinsicandextrinsicstackingfaultsareillustratedschematicallyinFigs2.8(e)and2.8(f),respectively.NotehowtheperfectABCABCstackingofatomsisdisturbedbytheinsertionorabsenceofrowsofatoms.2.3.4VolumeDefectsVolumedefectsareimperfectionssuchasvoids,bubble/gasentrapments,porosity,inclusions,precipitates,andcracks.Theymaybeintroducedintoasolidduringprocessingorfabricationprocesses.AnexampleofvolumedefectsispresentedinFig.2.9.ThisshowsMnSinclusionsinanA707steel.AnotherexampleofavolumedefectispresentedinFig.1.16(d).This ... Inc.whichisgivensimplybyÀðCAÀCBÞ=r0,thediffusionflux,J,maythenbeexpressedasJ¼D0expÀqkTdCdxð2:9ÞIfwescalethequantityqbytheAvogadronumber,thentheenergytermbecomesQ¼NAqandR¼kNA.Equation(2.9)maythusbeexpressedasJ¼ÀD0expÀQRTdCdxð2:10ÞIfwenowsubstituteD¼ÀD0expÀQRTintoEq.(2.10),weobtaintheusualexpressionforJ,i.e.,JisgivenbyJ¼ÀDdCdxð2:11ÞTheaboveexpressionisFick’sfirstlawofdiffusion.Itwasfirstpro-posedbyAdolfHicksin1855.Itisimportanttonoteherethatthediffusioncoefficientforself-diffusion,D,canhaveastrongeffectonthecreepproper-ties,i.e.,thetime -dependent owofmaterialsattemperaturesgreaterthan$0.3–0.5ofthemeltingtemperatureindegreesKelvin.Also,theactivationenergy,Q,inEq.(2.10)isindicativeoftheactualmechanismofdiffusion,whichmayinvolvethemovementofinterstitialatoms[Fig.2.11(a)]andvacancies[Fig.2.11(b)].Diffusionmayalsooccuralongfastdiffusionpathssuchasdislocationpipesalongdislocationcores[Fig.2.12(a)]orgrainboundaries[Fig.2.12(b)].This ... Inc.whichisgivensimplybyÀðCAÀCBÞ=r0,thediffusionflux,J,maythenbeexpressedasJ¼D0expÀqkTdCdxð2:9ÞIfwescalethequantityqbytheAvogadronumber,thentheenergytermbecomesQ¼NAqandR¼kNA.Equation(2.9)maythusbeexpressedasJ¼ÀD0expÀQRTdCdxð2:10ÞIfwenowsubstituteD¼ÀD0expÀQRTintoEq.(2.10),weobtaintheusualexpressionforJ,i.e.,JisgivenbyJ¼ÀDdCdxð2:11ÞTheaboveexpressionisFick’sfirstlawofdiffusion.Itwasfirstpro-posedbyAdolfHicksin1855.Itisimportanttonoteherethatthediffusioncoefficientforself-diffusion,D,canhaveastrongeffectonthecreepproper-ties,i.e.,thetime -dependent owofmaterialsattemperaturesgreaterthan$0.3–0.5ofthemeltingtemperatureindegreesKelvin.Also,theactivationenergy,Q,inEq.(2.10)isindicativeoftheactualmechanismofdiffusion,whichmayinvolvethemovementofinterstitialatoms[Fig.2.11(a)]andvacancies[Fig.2.11(b)].Diffusionmayalsooccuralongfastdiffusionpathssuchasdislocationpipesalongdislocationcores[Fig.2.12(a)]orgrainboundaries[Fig.2.12(b)].This...