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

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

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

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

6. 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 –Alternate anions and cations

7. cation anion Ionic Compounds

8. 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

9. 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

10. HCP: tetrahdral sites 4 sites/unit cell 2 sites/close-packed atom

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

12. 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

13. 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

14. Common Ionic Structure Types Rock salt (NaCl) –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

15. 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

16. 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

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

18. 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

19. 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

20. 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+