Types of Primary Chemical Bonds

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

2. Review: Common Metal Structures hcp bcc ccp (fcc) ABCABC not close-packed ABABAB • 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. Ionic Compounds • elements differing in electronegativity anion cation Ceramics

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. 2(rc + RA) 2RA Cubic Coordination: CN = 8 a

8. 2RA rc + RA Cuboctahedral: CN = 12 rc + RA = 2RA rc = RA rc/RA = 1

9. Radius Ratio Rules

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

12. Radius Ratio Rules sites occur within close-packed arrays common in ionic compounds if rc is smaller than fRA, then the space is too big and the structure is unstable

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 (CaF2) • Derive from cubic-close packed array of Ca2+ • 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; rc/RA = 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

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

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

22. Example: ZnS • S2- ~ 1.84 Å; Zn2+ ~ 0.60 – 0.57 Å; • rc/RA = 0.326 – 0.408 • Zn2+ is big enough for CN = 4 • S2- in close-packed array • Zn2+ 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

23. y y z = 0 z = 1 z = ½ z = ½ x x ZnS: Zinc Blende  CCP anions as CP atoms fill 4/8 tetr sites S2- x x x x

24. ZnS: Zinc Blende S2- Zn2+ CN(S2-) also = 4 RA/rc > 1  S2- certainly large enough for 4-fold coordination

25. Example: CaF2 (Fluorite) • F- ~ 1.3 Å; Ca2+ ~ 1.0 Å; • rc/RA = 0.77 • Ca2+ 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 • RA /rc> 1  fluorine could have higher CN than 4 • Ca:F = 1:2  all tetrahedral sites filled • Places Ca2+ in site of CN = 8 • Why CCP not HCP? - same reason as NaCl

26. Fluorite Ca2+ F- CN(F-) = 4 CN(Ca2+) = 8 [target]

27. CsCl • Cl- ~ 1.8 Å; Cs+ ~ 1.7 Å; • rc/RA = 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 • RA /rc> 1  chlorine ideally also has large CN • Ca:Cl = 1:1  all sites filled

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

29. Why do ionic solids stay bonded? • Pair: attraction only • Solid: repulsion between like charges • Net effect? Compute sum for overall all possible pairs Madelung Energy Sum over a cluster beyond which energy is unchanged For simple structures Single rij |Z1| = |Z2| a = Madelung constant Can show

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

31. Perovskite • Perovskite: ABO3 [B  boron] • A2+B4+O3 A3+B3+O3 A1+B5+O3 • CaTiO3 LaAlO3 KNbO3 • Occurs when RA ~ RO and RA > RB • Coordination numbers • CN(B) = 6; CN(A) = • CN(O) = 2B + 4A • CN’s make sense? e.g. SrTiO3 • RTi = 0.61 Å • RSr = 1.44 Å • RO = 1.36 Å above/below A 12 O B RTi/RO = 0.45 RSr/RO = 1.06 http://abulafia.mt.ic.ac.uk/shannon/ptable.php

32. Tolerance factor close-packed directions A B