国际晶体学空间群表部分

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1、InternationalTablesforCrystallography(2006).Vol.A,Spacegroup146,pp.494–497.R3C433TrigonalNo.146R3PattersonsymmetryR3¯HEXAGONALAXESOriginon3Asymmetricunit0≤x≤2;0≤y≤2;0≤z≤1;x≤(1+y)/2;y≤min(1−x,(1+x)/2)333Vertices0,0,01,0,02,1,01,2,00,1,02333320,0,11,0,12,1,11,2,10,1,132333333323Sy

2、mmetryoperationsFor(0,0,0)+set(1)1(2)3+0,0,z(3)3−0,0,zFor(2,1,1)+set333(1)t(2,1,1)(2)3+(0,0,1)1,1,z(3)3−(0,0,1)1,0,z33333333For(1,2,2)+set333(1)t(1,2,2)(2)3+(0,0,2)0,1,z(3)3−(0,0,2)1,1,z33333333Copyright©2006InternationalUnionofCrystallography494CONTINUEDNo.146R3Generatorsselect

3、ed(1);t(1,0,0);t(0,1,0);t(0,0,1);t(2,1,1);(2)333PositionsMultiplicity,CoordinatesReflectionconditionsWyckoffletter,(0,0,0)+(2,1,1)+(1,2,2)+Sitesymmetry333333General:9b1(1)x,y,z(2)¯y,x−y,z(3)¯x+y,x¯,zhkil:−h+k+l=3nhki0:−h+k=3nhh2hl:l=3nhh¯0l:h+l=3n000l:l=3nhh¯00:h=3nSpecial:noextr

4、aconditions3a3.0,0,zSymmetryofspecialprojectionsAlong[001]p3Along[100]p1Along[210]p1a=1(2a+b)b=1(−a+b)a=1(a+2b)b=1(−a−2b+c)a=1bb=1c332323Originat0,0,zOriginatx,0,0Originatx,1x,02Maximalnon-isomorphicsubgroupsI[3]R1(P1,1)1+IIa[3]P3(145)1;2+(1,2,2);3+(2,1,1)2333333[3]P3(144)

5、1;2+(2,1,1);3+(1,2,2)1333333[3]P3(143)1;2;3IIbnoneMaximalisomorphicsubgroupsoflowestindexIIc[2]R3(a=−a,b=−b,c=2c)(146);[4]R3(a=−2a,b=−2b)(146)Minimalnon-isomorphicsupergroupsI[2]R3(148);[2]¯R32(155);[2]R3m(160);[2]R3c(161);[4]P23(195);[4]F23(196);[4]I23(197);[4]P23(198);1[4

6、]I23(199)1II[3]P3(a=1(2a+b),b=1(−a+b),c=1c)(143)333495R3C433TrigonalNo.146R3PattersonsymmetryR3¯RHOMBOHEDRALAXESOriginon3Asymmetricunit0≤x≤1;0≤y≤1;0≤z≤1;z≤min(x,y)Vertices0,0,01,0,01,1,00,1,01,1,1Symmetryoperations(1)1(2)3+x,x,x(3)3−x,x,x496CONTINUEDNo.146R3Generatorsselected

7、(1);t(1,0,0);t(0,1,0);t(0,0,1);(2)PositionsMultiplicity,CoordinatesReflectionconditionsWyckoffletter,SitesymmetryGeneral:3b1(1)x,y,z(2)z,x,y(3)y,z,xnoconditionsSpecial:noextraconditions1a3.x,x,xSymmetryofspecialprojectionsAlong[111]p3Along[110¯]p1Along[21¯1¯]p1a=1(2a−b−c)b=1(−a

8、+2b−c)a=1(a+b−2c)b=ca=1(b−c)b=1(a+b+c)33223