2013晶体学第七章

ByheartSomeplaysaresosuccessfulthattheyrunforyearsonend,Inmanyways,thisisunfortunateforthepooractorswhoarerequiredtogoonrepeatingthesamelinesnightafternight.Onewouldexpectthemtoknowtheirpartsbyheartandneverhavecausetofalter.Yetthisisnotalwaysthecase.AfamousactorinahighlysuccessfulplaywasoncecastintheroleofanaristocratwhohadbeenimprisonedintheBastillefortwentyyears.Inthelastact,agaolerwouldalwayscomeontothestagewithaletterwhichhewouldhandtotheprisoner.Eventhoughthenoblewasexpectedtoreadtheletterateachperformance,healwaysinsistedthatitshouldbewrittenoutinfull.Onenight,thegaolerdecidedtoplayajokeonhiscolleaguetofindoutif,aftersomanyperformances,hehadmanagedtolearnthecontentsoftheletterbyheart.Thecurtainwentuponthefinalactoftheplayandrevealedthearistocratsittingalonebehindbarsinhisdarkcell.Justthen,thegaolerappearedwiththepreciousletterinhishands.Heenteredthecellandpresentedthelettertothearistocrat.Butthecopyhegavehimhadnotbeenwrittenoutinfullasusual.Itwassimplyablanksheetofpaper.Thegaolerlookedoneagerly,anxioustoseeifhisfellowactorhadatlastlearnthislines.Thenoblestaredattheblanksheetofpaperforafewseconds.Then,squintinghiseyes,hesaid:'Thelightisdim.Readthelettertome'.Andhepromptlyhandedthesheetofpapertothegaoler.Findingthathecouldnotrememberawordofthelettereither,thegaolerreplied:'Thelightisindeeddim,sire,Imustgetmyglasses.'Withthis,hehurriedoffthestage.Muchtothearistocrat'samusement,thegaolerreturnedafewmomentslaterwithapairofglassesandtheusualcopyoftheletterwithheproceededtoreadtotheprisoner.第七章晶体学空间群7.1点式空间群若平移群T在点群P的任意操作的相似变换下不变,则T与P可构成半直积群,即点式空间群(symmorphicspacegroup)。G=T∧PSyngony中心非中心非中心triclinic1(C1)monoclinic2/m(C2h)2(C2)m(Cs)orthorhombicmmm222(D2)mm2(C2v)trigonal3(C3)32(D3)3m(C3v)tetragonal4/m(C4h)4(C4)4/mmm(D4h)422(D4)4mm(C4v)hexagonal6/m(C6h)6(C6)6/mmm(D6h)622(D6)6mm(C6v)cubic23(T)432(O)1)(33iC)(dDm33)(3hTm)(3hOmm)(63hC)(242dDm)(263hDm)(34dTm)(44SSyngonyBravaislatticeLatticepointgroupPointgrouptriclinicaP1monoclinicmP,mS2/m2/m,2,morthorhombicoP,oI,oS,oFmmmmmm,222,mm2tetragonaltP,tI4/mmm4/m,4,4/mmm,422,4mm,cubiccP,cI,cF23432,hexagonalhP6/mmm6/m,6,6/mmm,622,6mm,trigonalhP6/mmm332,3m,hR13m3mm31m3)(63hC)(263hDm4m243mmm3m3411144444444晶系点阵点群P空间群三斜aP()1P1(1)(2)单斜mP(2/m)mC(2/m)2,m2/mP2(3)Pm(6)P2/m(10)C2(5)Cm(8)C2/m(12)正交oP(mmm)oC(mmm)oF(mmm)oI(mmm)222mm2mmmP222(16)Pmm2(25)Pmmm(47)C222(21)Cmm2(35)Amm2(38)Cmmm(65)F222(22)Fmm2(42)Fmmm(69)I222(23)Imm2(44)Immm(71)1P1P17.1.1三斜晶系空间群例举反演与平移的组合定理以o点为反演心先反演,再平移t,两步操作等效于对一个新反演心o’的反演,o’位于t/2(t/2的始点为o)。证:设平移矢a位于纸面,o为对称心。对o点{0,0,0}的反演等效于绕与纸面垂直并过o点的2重轴C2{0,0,z}的旋转与以纸面为反映面的反映之组合,a{0,0,0}=aC2{0,0,z}mh=C2'{a/2,0,z}mh={1/2,0,0}oaboabpp,-+,-+,-+,-+ABCD11_cell_length_a6.4227(4)_cell_length_b9.4246(5)_cell_length_c16.9326(9)_cell_angle_alpha83.890(3)_cell_angle_beta81.735(3)_cell_angle_gamma70.108(3)_cell_volume951.96(9)_cell_formula_units_Z27.1.2单斜晶系空间群例举_symmetry_cell_settingMonoclinic_symmetry_space_group_name_H-MP2_cell_length_a7.6924(15)_cell_length_b6.6543(13)_cell_length_c34.269(7)_cell_angle_alpha90.00_cell_angle_beta91.742(2)_cell_angle_gamma90.00_cell_volume1753.3(6)_cell_formula_units_Z2正交晶系空间群例举oaboobccao'o'b'a'b'a'(a'b'c')=(acb)(a'b'c')=(cba)()()()bcaNNN四方晶系例举Wyckoffletter区别晶胞中对称地位不同的位置,称为Wyckoffposition。acFeHg(SCN)4ac定理7-2:晶体结构中的分子(或原子团)只能处于位置点群为该分子的点群之子群的Wyckoff位置,即分子点群至少具有所在Wyckoff位置的对称性。B1O1AABBAO2O3O1'O2''12233bhac'bchrrarO4'=cabhhhcrbrarahchbhO1O4'cabhhhcrbrarahchbhO1O4'三方晶系例举_chemical_formula_moiety'C36H27N3‘_chemical_formula_weight501.61_symmetry_cell_settingHexagonal_symmetry_space_group_name_H-MR-3_cell_length_a22.6693(6)_cell_length_b22.6693(6)_cell_length_c8.9507(3)_cell_angle_alpha90.00_cell_angle_beta90.00_cell_angle_gamma120.00_cell_volume3983.5(2)_cell_formula_units_Z6_cell_measurement_temperature150(2)_refine_ls_number_reflns2008_refine_ls_number_parameters154_refine_ls_number_restraints0_refine_ls_R_factor_all0.0611_refine_ls_R_factor_gt0.0438_refine_ls_wR_factor_ref0.1145_refine_ls_wR_factor_gt0.1076_refine_ls_restrained_S_all0.969_refine_ls_shift/su_max0.001_diffrn_measured_fraction_theta_max987_diffrn_reflns_theta_full27.46_refine_diff_density_max0.198_refine_diff_density_min-0.1507.2非点式空间群G=T∧P'=T∧{(W1=I,w1=0);(W2,w2);(W3,w3);...,(Ws,ws)}=T+T(W2,w2)+T(W3,w3)+...+T(Ws,ws)晶系点阵与点阵点群点群P空间群单斜mP(2/m)mC(2/m)2,m,2/mP2,Pm,P2/m,C2,Cm,C2/mP21,Pc,P21/m,P2/c,P21/cCc,C2/c定理7-3:源于中心对称点群的点式和非点式空间群都是中心对称的。空间群的中心对称与否取决于其点群的中心对称与否。晶系点阵点群P空间群单斜mP(2/m)mC(2/m)2,m,2/mP2,Pm,P2/m,C2,Cm,C2/mP21,Pc,P21/m,P2/c,P21/cCc,C2/c定理7-3:空间群的中心对称与否取决于其点群的中心对称与否。P2/mW2W1=W3P21/c(W2,w2)(W1,w1)=(W2W1,W2w1+w2)P21群由P2=T∧{1;2{0,y,0}},可引伸出P21=T∧{1;(2{0,y,0},b/2)}C2=T∧{1,2}={(ua+vb+wc)∪(ua+vb+wc+a/2+b/2)}∧{1;2{0,y,0}}C21=T∧{1,21}={(ua+vb+wc)∪(ua+vb+wc+a/2+b/2)}∧{1;(2{0,y,0},b/2)}C21与C2为同一种空间群ETHgCl3Pc(Pc,Pa,Pn)晶系点阵点群P空间群单斜mP(2/m)mC(2/m)2,m,2/mP2,Pm,P2/m,C2,Cm,C2/mP21,Pc,P21/m,P2/c,P21/cCc,C2/cWhatistheanglebetweenthetwomoleculardipolemomentintheunitcell?Whatisthedirectionofthepolarizationvector?_symmetry_cell_settingMonoclinic_symmetry_space_group_name_H-MPn_symmetry_equiv_pos_as_xyz'x,y,