Chapter 9 Structural chemistry of ionic compounds 9.1 The ionic radii ratio and the coordination polyhedra of ions Interstices octahedral holes tetrahedral holes hole size is 0.414R hole size is 0.225R CN:6 CN:4
Chapter 9 Structural chemistry of ionic compounds 9.1 The ionic radii ratio and the coordination polyhedra of ions octahedral holes hole size is 0.414R CN: 6 tetrahedral holes hole size is 0.225R CN: 4 Interstices
Interstice type C.N. Thole/R Triangular 3 0.155 Tetrahedal 4 0.225 Octahedral 6 0.414 Cubic 8 0.732 Cuboctahedron 12 1.000 The rule of the packing of ions 88
Triangular 3 0.155 Tetrahedal 4 0.225 Octahedral 6 0.414 Cubic 8 0.732 Cuboctahedron 12 1.000 Interstice type C.N. rhole /R The rule of the packing of ions
Table 1.The limiting ratio of some coorrdination Coordination polyhedra C.N minimum r,/r. Triangular 3 0.155 Tetrahedal 4 0.225 Octahedral 6 0.414 Cubic 8 0.732 Cuboctahedron 12 1.000 9.2 The crystal structures of Some typical ionic compounds Answer the following questions: The packing style of anions The position of cations Crystal System (Bravais Lattice)? The C.N.of anion and cation Atom number in one unit cell? ·Structural formula? ·Atomic coordinates
Coordination polyhedra C.N. minimum r+/rTriangular 3 0.155 Tetrahedal 4 0.225 Octahedral 6 0.414 Cubic 8 0.732 Cuboctahedron 12 1.000 Table 1. The limiting ratio of some coorrdination 9.2 The crystal structures of Some typical ionic compounds Answer the following questions: • The packing style of anions ? • The position of cations ? • Crystal System (Bravais Lattice)? • The C.N. of anion and cation ? • Atom number in one unit cell? • Structural formula ? • Atomic coordinates
ZnS (0.225-0.414) CN+CN.-4:4 (Sphalerite) ·The packing of fec anions .Bravais Lattice Cubic F •The position of V2 Tetrahedral cations: holes Zn:S =4:4 cubic The C.N.of cation 4:4 and anion: A:0,0,0,1/2,1/2,0,1/2,0,1/2 0,1/2,1/2 ·Atom number in 4:4 B:3/4,1/4,1/4:1/4,3/4,1/4: one unit cell: 1/4,1/4,3/4;3/4,3/4,3/4 ZnS (0.225-0.414 (Wurtzite) ·The packing of hcp anions: .Bravais Lattice Hexagonal P .The position of 2 Tetrahedral cations: holes The C.N.of cation 4:4 and anion: Zn:S 2:2 hexagonal ·Atom number in 2:2 A:0,0,0,1/3,2/3,1/2 one unit cell: B:0,0,3/8,1/3,2/3,7/8 CuF,CuCl,CuBr,Cul;AgI;ZnO,ZnS,ZnSe,ZnTe;CdO,CdS, CdSe,CdTe;HgS,HgSe,HgTe
ZnS (0.225-0.414) C.N.+:C.N.- 4:4 (Sphalerite) Zn:S = 4:4 cubic A: 0,0,0; 1/2,1/2,0, 1/2,0,1/2; 0,1/2,1/2 B: 3/4,1/4,1/4; 1/4,3/4,1/4; 1/4,1/4,3/4; 3/4,3/4,3/4 •Bravais Lattice : Cubic F • Atom number in 4:4 one unit cell: The C.N. of cation 4:4 and anion: ½ Tetrahedral holes •The position of cations: • The packing of fcc anions: Zn:S = 2:2 hexagonal A: 0,0,0, 1/3,2/3,1/2 B: 0,0,3/8; 1/3,2/3,7/8 (Wurtzite) ZnS (0.225-0.414) CuF, CuCl, CuBr, CuI; AgI; ZnO, ZnS, ZnSe, ZnTe; CdO, CdS, CdSe, CdTe; HgS, HgSe, HgTe •Bravais Lattice : Hexagonal P • Atom number in 2:2 one unit cell: The C.N. of cation 4:4 and anion: ½ Tetrahedral holes •The position of cations: • The packing of hcp anions:
NaCl(0.732-0.414)Cubic,.C.N+c.N-66, ·The packing of fec anions .Bravais Lattice Cubic F .The position of Octahedral cations: holes The C.N.of 6:6 Na:Cl 4:4 cation and anion: A:0,0,0;1/2,1/2,0,1/2,0,1/2,0,1/2,1/2 ·Atom number 4:4 B:1/2,1/2,1/2;1/2,0,0:0,1/2,0,0,0,1/2 in one unit cell: (0.732-0.414)KCl,KBr,SrS,RbI,BaTe,SrSe,CaS,KI,SrTe,MgO, LiF,CaSe,NaBr,CaTe,MgS,NaI,LiCl,(>0.732)KF,SrO,BaO, RbF,RbCl,BaS,CuO,CsF,RbBr,BaSe,NaF,(<0.414)MgSe, LiBr,LiF NiAs(0.732-0.414) Hexagonal,C.N.+:C.N.6:6, (0.732-0.414)FeS
NaCl (0.732-0.414) Cubic, C.N.+:C.N.- 6:6, Na:Cl = 4:4 A: 0,0,0; 1/2,1/2,0, 1/2,0,1/2; 0,1/2,1/2 B: 1/2,1/2,1/2; 1/2,0,0; 0,1/2,0, 0,0,1/2 (0.732-0.414) KCl, KBr, SrS, RbI, BaTe, SrSe, CaS, KI, SrTe, MgO, LiF, CaSe, NaBr, CaTe, MgS, NaI, LiCl, (>0.732) KF, SrO, BaO, RbF, RbCl, BaS, CuO, CsF, RbBr, BaSe, NaF, (<0.414) MgSe, LiBr, LiF •Bravais Lattice : Cubic F • Atom number 4:4 in one unit cell: The C.N. of 6:6 cation and anion: Octahedral holes •The position of cations: • The packing of fcc anions: NiAs (0.732-0.414) Hexagonal, C.N.+:C.N.- 6:6, (0.732-0.414) FeS
TiO,(Rutile) Tetragonal C.N.+:C.N.=6:3 ·The packing of Distorted hep anions: .Bravais Lattice: Tetragonal P •The position of V2distorted cations: octahedral holes The C.N.of 6:3 cation and anion: ·Atom number in Ti:0=2:4 A:0,0,0:1/2,1/2,1/2(T1 one unit cell: B:u,u,0,-u,-u,0;1/2+u,1/2-u,1/2;1/2-u,1/2+u,1/2 (0.732-0.414)TeO2,MnF2,PbO2,FeF2,CoF2,ZnF2,NiF2,MgF2:SnO2, NbO2,MoO2,WO2,OsO2,IrO2,RuO2,TiO2,VO2,MnO2,GeO2 CsCl cubic,C.N.+:C.N.-8:8 ·The packing of Cubic anions: .Bravais Lattice Cubic P .The position of Cubic holes cations: The C.N.of 8:8 cation and anion: ·Atom number in 1:1 A:0,0,0 one unit cell: B:1/2,1/2,1/2 CsBr,CsI (1-0.732)
TiO2 (Rutile) Tetragonal C.N.+:C.N.- =6:3 A: 0,0,0; 1/2,1/2,1/2 (Ti) B: u,u,0, -u,-u,0; 1/2+u, 1/2-u, 1/2; 1/2-u, 1/2+u, 1/2 (0.732-0.414 ) TeO2, MnF2, PbO2, FeF2, CoF2, ZnF2, NiF2, MgF2, SnO2, NbO2, MoO2, WO2, OsO2, IrO2, RuO2, TiO2, VO2, MnO2, GeO2 •Bravais Lattice : Tetragonal P • Atom number in Ti:O = 2:4 one unit cell: The C.N. of 6:3 cation and anion: ½ distorted octahedral holes •The position of cations: • The packing of Distorted hcp anions: CsCl cubic, C.N.+:C.N.- 8:8 A: 0,0,0 B: 1/2,1/2,1/2 CsBr, CsI (1-0.732) •Bravais Lattice : Cubic P • Atom number in 1:1 one unit cell: The C.N. of 8:8 cation and anion: •The position of Cubic holes cations: • The packing of Cubic anions:
CaF,(Fluorite)AB,type C.N.+:C.N.=8:4 ·The packing of Cubic anions: .Bravais Lattice: Cubic F .The position of 2 Cubic cations: holes The C.N.of 8:4 cation and anion: ·Atom number in Ca:F=4:8 one unit cell: A:0,0,0:1/2,1/2,0,1/2,0,1/2;0,1/2,1/2 B:3/4,1/4,1/4;1/4,3/4,1/4,1/4,1/4,3/4;3/4,3/4,3/4 3/4,3/4,1/4,3/4,1/4,1/4,1/4,3/4,3/4,3/4,1/4,3/4 (>0.732)BaF2,PbF2,SrF2,HgF2,ThO2,CaF2,UO2,CeO2,PrO2,CdF2 (0.67)ZrF2,HfF2 Rb20,Li20 ---anti-Fluorite structure type The packing of anions? The position of cations? ·Bravais Lattice? ·TheC.N.of anion and cation? .Atom number in one unit cell?
CaF2 (Fluorite) AB2 type C.N.+:C.N.- =8:4 A: 0,0,0; 1/2,1/2,0, 1/2,0,1/2; 0,1/2,1/2 B: 3/4,1/4,1/4; 1/4,3/4,1/4; 1/4,1/4,3/4; 3/4,3/4,3/4 3/4,3/4,1/4; 3/4,1/4,1/4; 1/4,3/4,3/4; 3/4,1/4,3/4 (>0.732) BaF2, PbF2, SrF2, HgF2, ThO2, CaF2, UO2, CeO2, PrO2, CdF2; (0.67) ZrF2, HfF2 •Bravais Lattice : Cubic F • Atom number in Ca:F = 4:8 one unit cell: The C.N. of 8:4 cation and anion: ½ Cubic holes •The position of cations: • The packing of Cubic anions: Rb2O, Li2O --- anti- Fluorite structure type • The packing of anions? • The position of cations? • Bravais Lattice ? • The C.N. of anion and cation? •Atom number in one unit cell?
Typical Crystal Structures of Binary Component Structure Structure Anion Cation Coordination Name Type Packing position Numbers Examples Cations Anions Soldium AB FCC All octahedral 6 6 NaCl,MgO, Chloride holes FeO,LiF,Cao, Nio Cesium AB Simple cubic All cubic 8 8 CsCl chloride holes Zinc blende AB FCC 1/2 tetrahedral 4 ZnS,Sic (sphalerite) holes Wurtize AB HCP 1/2 tetrahedral 4 ZnS holes Fluorite AB2 Simple cubic 1/2 cubic 4 CaF2,ZrO2 holes Rutile AB2 HCP 1/2 octahedral 6 3 TiO2 MnO2 holes Sno2 CaTiO,(perovskite)ABX; a CaTiO; YBa2Cu3O7
CaF2 8 4 ,ZrO2 1/2 cubic holes Fluorite AB2 Simple cubic HCP HCP FCC Simple cubic FCC Anion Packing 1/2 tetrahedral 4 4 ZnS, SiC holes Zinc blende AB (sphalerite) TiO2, MnO2, SnO2 1/2 octahedral 6 3 holes Rutile AB2 1/2 tetrahedral 4 4 ZnS holes Wurtize AB All cubic 8 8 CsCl holes Cesium AB chloride NaCl, MgO, FeO,LiF, CaO, NiO All octahedral 6 6 holes Soldium AB Chloride Examples Coordination Numbers Cations Anions Cation position Structure Type Structure Name Typical Crystal Structures of Binary Component CaTiO3 (perovskite) ABX3 Ca Ti O YBa2Cu3O7 CaTiO3
MgAl2O (spinel) AB2X O anions form fcc lattice Mg2+cations (A)in 1/8 tetrahedral holes Al3+cations (B)in half of octahedral holes OB 00 eg.FeAl2O4,ZnAl2O4,MgAl2O4 anti-spinel B[AB]O magnetite (FeO)=spinel Fe3+(Fe3*,Fe2+)O=B(AB)O O anions form fcc lattice Fe3+(B)cations in 1/8 tetrahedral holes, (Fe3+,Fe2+)(A)cations in half of Octohedral Sites octahedral holes ●A Sites ⊙BSites Spinel [AlBBlO ○Oxygen Anti-spinel [BlAB]O Tetrahedral Sites eg.FeFe,O,FeMgFeO
MgAl2O4 (spinel) AB2X4 O anions form fcc lattice Mg2+cations (A) in 1/8 tetrahedral holes Al3+ cations (B) in half of octahedral holes eg. FeAl2O4, ZnAl2O4, MgAl2O4 anti-spinel B[AB]O4 eg. FeFe2O4, FeMgFeO4 magnetite (Fe3O4) = spinel ( Fe3+(Fe3+,Fe2+)O4 = B(AB)O4 O anions form fcc lattice Fe3+ (B) cations in 1/8 tetrahedral holes, (Fe3+,Fe2+) (A) cations in half of octahedral holes Spinel [A]t [BB]oO4 Anti-spinel [B]t [AB]oO4
Summary of Some Common Crystal Structures Structure Structure Anion Cation Coordination Name Type Packing position Numbers Examples Cations Anions Rock Salt AB FCC All octahedral 6 6 NaCl,MgO, holes FeO,LiF,CaO, NiO Cesium AB Simple cubic All cubic 8 8 CsCI chloride holes Zinc blende AB FCC 1/2 tetrahedral 4 ZnS,Sic (sphalerite) holes Wurtize AB HCP 1/2 tetrahedral 4 ZnS holes Fluorite AB2 Simple cubic 1/2 cubic 8 CaF2:ZrO2 holes Rutile AB2 HCP 1/2 tetrahedral 6 3 TiO2,MnO2, holes SnO2 Perovskite ABX3 FCC(A and X) All octahedral 12(A) 6 BaTiO3,SrTiO, holes for B 6(B) Spinel AB2X4 FCC 1/8 octahedral 4A) MgALO holes for A 6(B)】 1/2 tetrahedral FeAl2O4 holes 9.3 Lattice energy The calculation and determination of lattice energy Na+(g)+Cl-(g)--->NaCl (s)+U (Na)= .Ze6+l2Z+8+62+J 一6+ 4πE 2 Z34 Z Z.Ze2 12.86 -「6- 4πEo' +... V25√4 Z.ZeA Na 4πer A≈1.7476，Madelung constant
CaF2 8 4 ,ZrO2 1/2 cubic holes Fluorite AB2 Simple cubic FCC FCC(A and X) HCP HCP FCC Simple cubic FCC Anion Packing 1/2 tetrahedral 4 4 ZnS, SiC holes Zinc blende AB (sphalerite) BaTiO3 6 , SrTiO3 12(A) 6(B) All octahedral holes for B Perovskite ABX3 MgAl2O4 FeAl2O4 4(A) 4 6(B) 1/8 octahedral holes for A 1/2 tetrahedral holes Spinel AB2X4 TiO2, MnO2, SnO2 1/2 tetrahedral 6 3 holes Rutile AB2 1/2 tetrahedral 4 4 ZnS holes Wurtize AB All cubic 8 8 CsCl holes Cesium AB chloride NaCl, MgO, FeO,LiF, CaO, NiO All octahedral 6 6 holes Rock Salt AB Examples Coordination Numbers Cations Anions Cation position Structure Type Structure Name Summary of Some Common Crystal Structures 9.3 Lattice energy The calculation and determination of lattice energy Na+(g) + Cl- (g) ---Æ NaCl (s) + U 1.7476, Madelung constant 4 ...] 4 6 3 8 2 12 [6 4 ...] 4 6 3 8 2 12 [6 4 ( ) 0 2 0 2 0 2 ≈ = = − + − + = + + + + + − + − − + − + + − + A A r Z Z e r Z Z e Z Z Z Z r Z Z e Na πε πε πε ε r r