准晶理论的新进展

3(:59772015)2000-03-24,2000-05-173(100080)2nm,.,Gummelt1995,,Penrose.,.,.Gummelt1999,,,.,,,RECENTPROGRESSOFQUASICRYSTALTHEORYGUOKe2Xin(K.H.Kuo)(InstituteofPhysics,BeijingLaboratoryofElectronMicroscopy,ChineseAcademyofSciences,Beijing100080)AbstractThehigh2resolutionelectronmicroscopicimagesofquasicrystalsveryoftenshowoverlappeddecago2naldiscsofabout2nmindiameter.Basedonthisobservation,Gummeltin1995designedatwo2coloureddecagonwhichcanbeoverlappedwithneighbouringones.Ifthecoveringregionoftwodecagonshasthesamecolouredparts,itcanbeproventhatthiscoveredpattern,likePenrosepattern,isaquasiperiodicone.Suchaquasiperiodiccoveringrequiresonlyonequasi2unitcellandthecoveredregionservesasanucleusoftheformationoftheneighbouringquasi2unitcell.Gummeltin1999removedthecolourinthedecagon,andsuchacoveredpatterncouldbeperiodic,quasi2periodic,orsomethingintermediatebetweenthem.Keywordsquasicrystal,decagon,covering,approximant1Penrose(1974)[1]1984,Penrose(1)[1],PenrosePenrose.(p),36(s),(h)(b)(tile)(tiling).,,,.,(aperiodic),.,,=(1+5)/2=1/(2cos72),Penrose.,Penrose,.,Penrose.,,,,.,Penrose.(Penrose[2]),?,?,807©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1Penrose()[1][p36h,bs.()72H,B,S.HBD,D,H]Penrose.,Al-Co-CuAl-Ni-Cu2nm,.Burkov[3].2(Gummelt[4])[A(be)H(b),B(c,d)(),BS(e)().B(f),H,B]2Gummelt(1995)[4]Penrose,Gummelt,(covering)[46].,[2(a)],HB.,,.,.2,H(A),2(be),(B),2(f).2(b),H;2(c,d),(B);2(e),B,S,.2(f),,.,72H,72B72SHBS.1Penrose,36h6H,36b872B,36s1072S(1).HBD,,H,B,SPenrose.,GummeltPenrose[5,6]..,,.,,.,,.,.,,.,..GummeltPenrose,,[5]1995,[7][7][911].Gummelt[1215].3Ga-Mn[15],,H,B,S.,,bf,2(bf).3Gummelt(1999)[16],90729(2000)12©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3Ga-Mn()[15][B,H,SD(2nm).Dbf2bf,beA,fB.cDBH(),cBd.eDB,S,DH().4D,H(b),B(f).H(),S().]Penrose,.,Penrose,H,72B,72S.H,B,S,,(crystallineapproximant).,,1990[15,1723].4(a)1992Al3Mn[17],Al3Mn4Y.H,4(b)Al3Mn.,4(a)B,H,Al3Mn.B.Ga-MnB(5)B[19],HB(6)[20],[21].,C31Al60Mn114[(a)Al3Mn[010][17].H,Al3Mn(010)(Y)(010);(b)Mn,10Al()[17],(a)HB,H;(c)Gummelt(1999)[16]H(),(b)Al3Mn(010)],H72S[22].1997,6,4Ga-MnHB,[15].Gummelt[24].7,Gummelt,,[16],H,B,S,,4(c)HAl3Mn(010),4(b).1),017©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.B(5)1S+2HH,B,S,.GummeltH,B,S.1)P.Gummelt5Ga-Mn[010][19][B,(010)(3).[010].,]6Ga7Mn5[010][19][BH.BH,(010)(3).]Gummelt19999,.Penrose,.,Gummelt.(phason)/,Pen2rose7236.PenroseGummelt.,Gummelt,.Gummelt[16]..[1]PenroseR.Bull.Inst.Math.Appl.,1974,10:266[2]PenroseR.Eureka,1978,39:16;Math.Intell.,1979,2:32[3]BurkovSE.Phys.Rev.Lett.,1991,67:614[4]GummeltP.In:Proc.5thInt.Conf.onQuasicrystals.Avignon,1995.84[5]GummeltP.GeometriaeDedicata,1996,62:1[6]GummeltP.ThesisPhD.AperiodischeUberdeckungenmiteinemClustertyp.ShakerVerlag,Aachen,1999[7]Ben2AbrahamSI,G¾hlerF.Phys.Rev.,1999,60:860[8]G¾hlerF.In:Proc.7thInt.Conf.onQuasicrystals,Stuttgart,1999[9]SteinhardtPJ,JeongH2C.Nature,1996,382:431[10]JeongH2C,SteinhardtPJ.Phys.Rev.,1997,B55:3520[11]LordEA,RanganathanS,KulkarniUD.In:Proc.7thInt.Conf.onQuasicrystals,Stuttgart,1999[12]SteinhardtPJ,JeongH2C,SaifokKetal.Nature,1998,396:55[13]SaifokK,TsudaK,TanakaM.J.Phys.Soc.Japan,1998,67:2578[14]YanY,PennycookSJ,TsaiAP.Phys.Rev.Lett.,1998,81:5145[15]WuJS,KuoKH.In:TakeuchiS,FujiweraTeds.Proc.6thInt.Conf.onQuasicrystals.Singapore:WorldScientific,1998.215[16]GummeltP,BandtC.In:Proc.7thInt.Conf.onQuasicrystals.Stuttgart,1999[17]LiXZ,ShiD,KuoKH.Phil.Mag.1992,B66:331[18]WuJS,LiXZ,KuoKH.Phil.Mag.Lett.,1998,77:359[19]WuJS,GeSP,KuoKH.Phil.Mag.,1999,A79:1787[20]WuJS,KuoKH.Micron,inpress[21]GeSP,KuoKH.Metall.Mater.Trans.1999,30A:697[22]SuiHX,SunK,KuoKH.Phil.Mag.,1997,A75:379[23].,1998,27:515[GUOKe2Xin.Wuli(Physics),1998,27:515(inChinese)][24]GummeltP.In:TakeuchiS,FujiweraTeds.Proc.6thInt.Conf.onQuasicrystals.Singapore:WorldScientific,Singapore1998.14811729(2000)12©1995-2006TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.