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Ionic Bonding & Structures

Ionic Bonding & Structures. Isotropic bonding Maximize # of bonds, subject to constraints Maintain stoichiometry; Alternate anions and cations Like atoms should not touch. ‘Radius Ratio Rules’. –. –. –. –. . –. –. +. –. –. +. –. –. –. –. –. –. –. +. –. –. –.

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Ionic Bonding & Structures

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  1. Ionic Bonding & Structures • Isotropic bonding • Maximize # of bonds, subject to constraints • Maintain stoichiometry; Alternate anions and cations • Like atoms should not touch ‘Radius Ratio Rules’ – – – –  – – + – – + – – – – – – – + – – – Just barely stable

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

  3. 2RA rc + RA Cuboctahedral: CN = 12 rc + RA = 2RA rc = RA rc/RA = 1

  4. Radius Ratio Rules if rc is smaller than fRA, then the space is too big and the structure is unstable

  5. Ionic Compounds anion cation Ceramics

  6. 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

  7. 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

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

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

  10. 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

  11. 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

  12. 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

  13. 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

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

  15. 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

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

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