材料热力学与动力学-3

Chapter3:CrystalInterfacesandMicrostructure3-1Chapter3.CrystalInterfacesandMicrostructureProf.Dr.X.B.ZhaoDepartmentofMaterialsScienceandEngineeringZhejiangUniversityChapter3:CrystalInterfacesandMicrostructure3-2FreeSurfaces(solid/vapourinterface)GrainBoundaries(a/ainterface)InterphaseInterfaces(a/binterface)MetallographicSurfacesBasicInterfaceTypesChapter3:CrystalInterfacesandMicrostructure3-3liquidfilmFAg:freeenergyperunitareaG=G0+AgFA+dAdG=gdA+Adg=FdA(worddonebyF)ifg=const.,F=g(surf.tension=surf.energy)dimension:Jm-23.1InterfacialFreeEnergyChapter3:CrystalInterfacesandMicrostructure3-4whatdoesthesurfaceenergyoriginatefrom?——brokenbondsee/2e/2Ls=ZNae/2Ls:sublimationheatZ:numberofnearestneighborsNa:Avogadro’snumber=6.0221023mol-13.2Solid/VapourInterfacesChapter3:CrystalInterfacesandMicrostructure3-5higherorirrational{hkl}index?asteppedlayersofclose-packedplanesq(cosq)/abrokenbonds(sin|q|)/abrokenbonds1/abrokenbondsperunitsurfacewithacrystalplaneatanangleqtotheclose-packedplane:(cosq+sin|q|)/a2High-indexedsurfaceChapter3:CrystalInterfacesandMicrostructure3-6(001)(111)(110)OgAAg-plotofasectionin3DorientationspacesurfaceinrealspacenormaltoOAg-plotChapter3:CrystalInterfacesandMicrostructure3-7SurfaceEquilibriumofaIsolatedParticlea)surfaceswithlowerenergiesspeciallyorientedsurfaces(close-packedorientations)b)reductionofthetotalsurfacetendingtoasphereSurfaceEquilibriumChapter3:CrystalInterfacesandMicrostructure3-8SnparticlesonNaClNiCrcrystalonThO2NicrystalonThO2IrcrystalinHeg:abcdEquilibriumcrystallineshapesChapter3:CrystalInterfacesandMicrostructure3-9descriptionofagrainboundarya)orientationdifferencebetweentwograins3freedomsb)boundaryorientationinthesamplespace2freedomsgrainboundaryenergyorigin:crystallinedefectsorder:0.1eV/atomor0.5J/m23.3BoundariesinSingle-PhaseSolidsChapter3:CrystalInterfacesandMicrostructure3-10q001a010a100a100bqboundaryplanegrainboundary//rotationaxisTiltboundariesChapter3:CrystalInterfacesandMicrostructure3-11qedgedislocationsDqbDqqbbDtanLow-angletiltboundariesChapter3:CrystalInterfacesandMicrostructure3-12screwdislocationsgrainboundaryrotationaxisqTwistboundariesChapter3:CrystalInterfacesandMicrostructure3-13acoherenttwinboundaryanincoherenttwinboundaryfTwinboundaries(large-angle)Chapter3:CrystalInterfacesandMicrostructure3-14grainboundarytransitionzoneafewatomplanesthickLarge-anglegrainboundariesChapter3:CrystalInterfacesandMicrostructure3-15Large-&low-angleboundariesChapter3:CrystalInterfacesandMicrostructure3-16boundaryenergy,gmisorientation,q10~15°qgforlow-anglegrainboundariesrandomhigh-angleGBsggsv/3MisorientationandboundaryenergyChapter3:CrystalInterfacesandMicrostructure3-17Crystalgb/mJm-2T/°Cgb/gsvSn1642230.24Al3244500.30Ag3759500.33Au37810000.27Cu6259250.36g-Fe75613500.40d-Fe46814500.23Pt66013000.29W108020000.41measuredgrainboundaryfreeenergiesChapter3:CrystalInterfacesandMicrostructure3-18measuredgrainboundaryenergiesinAl10230.51.51.002080604060120180relativeboundaryenergymisorientation,qdeg.misorientation,qdeg.rotationaxis||100rotationaxis||11070.5twinChapter3:CrystalInterfacesandMicrostructure3-19microstructureofausteniticstainlesssteellarge-anglelow-anglecoherenttwinincoherenttwinVariousgrainboundariesChapter3:CrystalInterfacesandMicrostructure3-20grainsandgrainboundariesGrains——3D,butweseeonlysections2grainsagrainboundaryalineinthesection3grainsagrainedgeatriple-pointinthesection4grainsagraincornerinvisibleinthesectionChapter3:CrystalInterfacesandMicrostructure3-21whygrainboundariesexist?GBs:high-energyregionsinthestructure,increaseGrelativetoasinglecrystalGBs:adjustthemselvesmetastableequilibriumimportantaGBcouldnotstopinagrainGBsaregenerallymobilelocalequilibriumholdsinGBsChapter3:CrystalInterfacesandMicrostructure3-22howcouldaboundarydisappear?GBs:boundariesbetweendifferentorientatedgrainscoulddisappearonlybythegradualmigration012341234012340GBs’migrationiscoordinatedwiththetriplepointsGBs’numberremainsconstantifnograindisappear3GBsdisappearwhenagraindisappearChapter3:CrystalInterfacesandMicrostructure3-23BoundaryEnergytheequilibriumofGBsattriplepointsg:boundaryenergy,J/m2(energy)boundarytension,N/m(force)123g12g23g31q1q2q3312231123sinsinsinqgqgqgEquilibriumofGBsChapter3:CrystalInterfacesandMicrostructure3-24BoundaryEnergytheboundarycurvaturesifg=const.,qshouldbe120°q120°qboundariescurveq=120°qin2D:convexboundariesforn6concaveboundariesforn6BoundarycurvaturesChapter3:CrystalInterfacesandMicrostructure3-25anglebetween2edgesatacorner:109°28’anglebetween2facesataedge:120°grainsshouldbeabeletofillthespacetetradecahedrona-Kelvin’stetradecahedron109°28’120°b-Kelvin’stetradecahedronGrainShapesin3DChapter3:CrystalInterfacesandMicrostructure3-26BACDEFBAFCDEBAFCDEBFCDE7783477575TopologicalconsiderationsChapter3:CrystalInterfacesandMicrostructure3-275775onecycleonegrainvanishedthreeboundariesdisappearedthe“5-7pair”movesonesteptheaveragenumberofsidespergrainkeepconstant(n=6for2Dsystems)Chapter3:CrystalInterfacesandMicrostructure3-2