软物质与功能材料(刘向阳)2

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1、软物质及功能材料(5)SymmetryofCrystals&ThermodynamicsofCrystallization刘向阳，姜源厦门大学材料学院OutlineCrystalsymmetry-Thestructuresofcrystals7crystalsystems;14BravaisLattices230spacegroupsThermodynamicsofcrystallization-Howdoescrystallizationtakeplace?Recaptureofthermodynamics:Gibbsfreeenergy,chemicalpotential

2、,phaseequilibrium,phasediagramRecaptureofsomekeyconceptsScrewSymmetry(HelicalSymmetry):LeftandRight-handed•Whatistherotationalangleandthetranslation(infractionsofthepitch)?•Whatisthetotalnumberofmotifs?(1)(2)(3)(4)(5)MultipleSymmetryRelationshipsandPointGroups(cont’d)Pointsymmetrygroups(point

3、groups):Symmetryoperationofpointgroupsleaveatleastonesinglepointofspaceunmoved.Wehaveintotal32crystallographicpointgroupsinthecrystalregime.Thepointgroup6/mmmCrystallographicpointgroupThereareinfinitelymanythreedimensionalpointgroups;incrystallography,however,theyarerestrictedtobecompatiblew

4、iththediscretetranslationsymmetriesofacrystallattice.Only32crystallographicpointgroups.Intheclassificationofcrystals,eachpointgroupcorrespondstoacrystalclass-32crystalclasses.DescriptionofCrystalStructuresCrystallattice:AsetofpointstodescribetheSimplecubicsymmetryofacrystalstructure.Unitce

5、ll:thesmallestunittodescribethesymmetryofcrystalCubicClosedPackedstructure.DifferentCrystalStructures(http://cst-www.nrl.navy.mil/lattice/index.html)HexagonalBodyCenteredCubicclosedpackedCrystalSystems-7uniquecrystalsystemsThecrystalsystemsareagroupofcrystalstructuresaccordingtotheaxialsyste

6、musedtodescribetheirlattice.Eachcrystalsystemconsistsofasetofthreeaxesinaparticulargeometricalarrangement.=b,cTherearesevenunique=a,ccrystalsystems.=a,bDescriptionofCrystalStructuresL=ma+nb+pc,m,n,p:anyintegral7crystalsystemsCrystalaxesAnglesbetweenaxesTri-clinic(a)a,b,c,unrestricted.

7、Mono-clinic(b)a,b,c,unrestricted.==90oOrtho-rhombic(c)abc,===90oTetra-gonal(d)a=bc,===90oTri-gonal(e)a=b=c,==90oHexa-gonal(f)a=bc,==90o,=120oCubic(g)a=b=c,===90oDescriptionofCrystalStructuresAmongthe7crystals