1. Metallic –Electropositive: give up electrons Ionic –Electronegative/Electropositive Colavent –Electronegative: want electrons –Shared electrons along bond direction Types of Primary Chemical Bonds Isotropic, filled outer shells +-+ -+- +-+ +++ +++ +++ e- Close-packed structures

2. Review: Common Metal Structures hcp ccp (fcc) bcc ABABAB ABCABCnot close-packed Features Filled outer shells  spherical atom cores, isotropic bonding Maximize number of bonds  high coordination number High density

3. Metals single element, fairly electropositive elements similar in electronegativity

4. cation anion Ionic Compounds elements differing in electronegativity

5. Ionic Bonding & Structures Isotropic bonding Maximize packing density Maximize # of bonds, subject to constraints –Like atoms should not touch –Maintain stoichiometry –Alternate anions and cations

6. Ionic Bonding & Structures + – – – – – – + – – – – – – Isotropic bonding; alternate anions and cations – – – – – – + Just barely stable  Radius Ratio “Rules”

7. Cubic Coordination: CN = 8 2R A 2(r c + R A ) a

8. Cuboctahedral: CN = 12 r c + R A = 2R A r c = R A  r c /R A = 1 2R A r c + R A

9. Radius Ratio Rules CN (cation)Geometrymin r c /R A 2none (linear) 30.155 (trigonal planar) 40.225 (tetrahedral)

10. CNGeometrymin r c /R A 60.414 (octahedral) 80.732 (cubic) 121 (cuboctahedral)

11. Ionic Bonding & Structures Isotropic bonding Maximize # of bonds, subject to constraints –Like atoms should not touch ‘Radius Ratio Rules’ – rather, guidelines Develop assuming r c < R A But inverse considerations also apply n-fold coordinated atom must be at least some size –Maintain stoichiometry Simple A a B b compound: CN(A) = (b/a)*CN(B) –Alternate anions and cations

12. Radius Ratio Rules CN (cation)Geometrymin r c /R A ( f ) 2linearnone 3trigonal planar0.155 4tetrahedral0.225 6octahedral0.414 8cubic0.732 12cubo-octahedral1 if r c is smaller than f R A, then the space is too big and the structure is unstable common in ionic compounds sites occur within close-packed arrays

13. Local Coordination  Structures Build up ionic structures from close- packed metallic structures Given range of ionic radii: CN = 4, 6, 8 occur in close- packed structures tetrahedral octahedral

14. HCP: tetrahedral sites 4 sites/unit cell 2 sites/close-packed atom

15. HCP: octahedral sites 2 sites/unit cell 1 site/close-packed atom

16. Sites in cubic close-packed 8 tetrahedral sites/unit cell 2 tetrahedral sites/close-packed atom 4 octahedral sites/unit cell 1 octahedral site/close-packed atom

17. Summary: Sites in HCP & CCP 2 tetrahedral sites / close-packed atom 1 octahedral site / close-packed atom sites are located between layers: number of sites/atom same for ABAB & ABCABC

18. Common Ionic Structure Types Rock salt (NaCl) sometimes also ‘Halite’ –Derive from cubic-close packed array of Cl - Zinc blende (ZnS) –Derive from cubic-close packed array of S = Fluorite (CaF 2 ) –Derive from cubic-close packed array of Ca 2+ Cesium chloride (CsCl) –Not derived from a close-packed array Complex oxides –Multiple cations

19. Example: NaCl (rock salt) Cl - ~ 1.81 Å; Na + ~ 0.98 Å; r c /R A = 0.54 Na + is big enough for CN = 6 –also big enough for CN = 4, but adopts highest CN possible Cl - in cubic close-packed array Na + in octahedral sites Na:Cl = 1:1  all sites filled CN f 40.225 60.414 80.732

20. Rock Salt Structure Cl Na CN(Cl - ) also = 6 R A /r c > 1  Cl - certainly large enough for 6-fold coordination ccp array with sites shown

21. Lattice Constant Evaluation ccp metal 4R =  2 a a R a R a = 2(R A + r c ) > ( 4/  2)R A rock salt

22. Example: ZnS S 2- ~ 1.84 Å; Zn 2+ ~ 0.60 – 0.57 Å; –r c /R A = 0.326 – 0.408 Zn 2+ is big enough for CN = 4 S 2- in close-packed array Zn 2+ in tetrahedral sites Zn:S = 1:1  ½ tetrahedral sites filled Which close-packed arrangement? –Either! “Polytypism” –CCP: Zinc blende or Sphaelerite structure –HCP: Wurtzite structure CN f 40.225 60.414 80.732

23. ZnS: Zinc Blende x y z = 0 z = ½ x y z = 1 z = ½ x S 2- x x x  CCP anions as CP atoms fill 4/8 tetr sites

24. ZnS: Zinc Blende CN(S 2- ) also = 4 R A /r c > 1  S 2- certainly large enough for 4-fold coordination S 2- Zn 2+

25. Example: CaF 2 (Fluorite) F - ~ 1.3 Å; Ca 2+ ~ 1.0 Å; –r c /R A = 0.77 Ca 2+ is big enough for CN = 8 –But there are no 8-fold sites in close-packed arrays Consider structure as CCP cations –F - in tetrahedral sites –R A / r c > 1  fluorine could have higher CN than 4 Ca:F = 1:2  all tetrahedral sites filled Places Ca 2+ in site of CN = 8 Why CCP not HCP? - same reason as NaCl CN f 40.225 60.414 80.732

26. Fluorite CN(F - ) = 4 CN(Ca 2+ ) = 8 [target] F-F- Ca 2+

27. CsCl Cl - ~ 1.8 Å; Cs + ~ 1.7 Å; –r c /R A = 0.94 Cs + is big enough for CN = 8 –But there are no 8-fold sites in close-packed arrays CsCl unrelated to close-packed structures –Simple cubic array of anions –Cs + in cuboctahedral sites –R A / r c > 1  chlorine ideally also has large CN Ca:Cl = 1:1  all sites filled

28. Cesium Chloride Cl - Cs + 1 Cs + /unit cell 1 Cl - /unit cell CN(Cs) = 8

29. Why do ionic solids stay bonded? Solid: repulsion between like charges Net effect? Compute sum for overall all possible pairs Pair: attraction only Sum over a cluster beyond which energy is unchanged Madelung Energy Can show For simple structures Single r ij |Z 1 | = |Z 2 |  = Madelung constant

30. Structures of Complex Oxides Multiple cations –Perovskite Capacitors Related to high Tc superconductors –Spinel Magnetic properties Covalency –Zinc blende Semiconductors –Diamond Semiconductors –Silicates Minerals

31. Perovskite –Perovskite: ABO 3 [B  boron] A 2+ B 4+ O 3 A 3+ B 3+ O 3 A 1+ B 5+ O 3 CaTiO 3 LaAlO 3 KNbO 3 Occurs when R A ~ R O and R A > R B Coordination numbers –CN(B) = 6; CN(A) = –CN(O) = 2B + 4A CN’s make sense? e.g. SrTiO 3 –R Ti = 0.61 Å –R Sr = 1.44 Å –R O = 1.36 Å http://abulafia.mt.ic.ac.uk/shannon/ptable.php 12 above/below R Ti /R O = 0.45 R Sr /R O = 1.06 A B O

32. Tolerance factor close-packed directions A B