32晶体点群图示.ppt

32 crystallographic point gropsWith Gif AnimationsThe 32 crystallographic point groups(point groups consistent with translational symmetry)32 Point groups can be constructedFrom 11 initial pure rotational point groupsinversion centers can be added to produce an additional 11 centrosymmetric point groupsFrom the centrosymmetric point groups an additional 10 symmetries can be discoveredCyclic Point GroupsSym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Cyclic+Horizontal Mirror GroupsSym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Cyclic+Vertical Mirror GroupsSym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Rotoreflection GroupsSym.Elem.Sym.Elem.Sym.Ebination of rotations with other rotations in other directionsAllowed Combinations of Pure Rotations：Rotations+Perpendicular 2-foldsDihedral(Dn)GroupsSym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Dihedral Groups+shSym.Elem.Sym.Elem.Sym.Elem.Sym.Elem.Dihedral Groups+sdSym.Elem.Sym.Elem.Isometric Groups Roto-Combination with no Unique AxisT GroupsO GroupsT GroupsSym.Elem.Sym.Elem.Sym.Elem.O GroupsSym.Elem.Sym.Elem.crystallographic Point groups into 7 lattice systemsFlowchart for Determining SignificantPoint Group Symmetry14 Bravais lattice types into 7 lattice systems Table of space groups in 3Dreferences1.Lecture Notes,The Univ.of Texas at Austin2.http:/materials.cmu.edu/degraef/pg/pg.html3.G.Burns,Space Groups for Solid State Physics4.http:/en.wikipedia.org/wiki/Crystal_system5.http:/en.wikipedia.org/wiki/Space_group