Ionic Structures

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Ionic Structures

• Isotropic bonding
• Maximize of bonds, subject to constraints
• Maintain stoichiometry
• Alternate anions and cations
• Like atoms should not touch
• Radius Ratio Rules rather, guidelines
• Develop assuming rc lt RA
• But inverse considerations also apply
• Many can be described as close-packed anion
  array, with cations in interstitial sites

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Sites in close-packed structures

• Given range of ionic radii CN 4, 6, 8

occur in close-packed structures
tetrahedral
octahedral
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HCP tetrahdral sites
4 sites/unit cell 2 sites/close-packed atom
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HCP octahedral sites
2 sites/unit cell 1 site/close-packed atom
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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
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Radius Ratio Rules
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Example NaCl (rock salt)

• Cl- 1.81 Å Na 0.98 Å rc/RA 0.54
• Na is big enough for CN 6 (but not 8)
• also big enough for CN 4, but adopts highest CN
  possible
• Cl- in cubic close-packed array
• Na in octahedral sites
• NaCl 11 ? all sites filled
• Why CCP not HCP? - homework

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Rock Salt Structure
CN(Cl-) also 6 RA/rc gt 1 ? Cl- certainly large
enough for 6-fold coordination
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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
• ZnS 11 ? ½ tetrahedral sites filled
• Which close-packed arrangement?
• Either! Polytypism
• CCP Zinc blende or Sphaelerite structure
• HCP Wurtzite structure

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Zinc Blende (4/8 tetr sites filled)
S2-
x
x
x
x
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Zinc Blende
S2-
Zn2
CN(S2-) also 4 RA/rc gt 1 ? S2- certainly large
enough for 4-fold coordination
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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 / rcgt 1 ? fluorine could have higher CN than 4
• CaF 12 ? all tetrahedral sites filled
• Why CCP not HCP? - same reason as NaCl

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Fluorite
Ca2
F-
CN(F-) 4 CN(Ca2) 8 target
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Lattice Constant Evaluation
rock salt
ccp metal
a
R
4R ?2 a
a 2(RA rc) gt ( 4/?2)RA
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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 / rcgt 1 ? clorine ideally also has large CN
• CaCl 11 ? all sites filled

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Cesium Chloride
Cl-
1 Cs/unit cell 1 Cl-/unit cell CN(Cs) 8
Cs
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Hexagonal close-packed
2 sites/unit cell 1 site/close-packed atom
4 sites/unit cell 2 sites/close-packed atom
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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
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Structures of Complex Oxides

• Complex because
• Multiple cations
• Covalency effects
• Multiple cations
• Perovskite ABO3 B ? boron
• Goldschmidt tolerance factor
• Spinel
• Magnetic properties