cation

1
Ionic Compounds
anion
cation
Ceramics
2
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

3
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
4
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
5
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

6
ZnS Zinc Blende
? CCP anions as CP atoms fill 4/8 tetr sites
x
x
x
x
7
ZnS Zinc Blende
S2-
Zn2
CN(S2-) also 4 RA/rc gt 1 ? S2- certainly large
enough for 4-fold coordination
8
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
• Places Ca2 in site of CN 8
• Why CCP not HCP? - same reason as NaCl

9
Fluorite
Ca2
F-
CN(F-) 4 CN(Ca2) 8 target
10
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

12
Cesium Chloride
Cl-
1 Cs/unit cell 1 Cl-/unit cell CN(Cs) 8
Cs
13
Unit Cells Lattice Points
CsCl Structure
BCC Metal
How many lattice points per unit cell?
14
Structures of Complex Oxides

• Multiple cations
• Perovskite ABO3
• Capacitors
• Spinel
• Magnetic properties

• Covalency
• Zinc blende
• Semiconductors
• Diamond
• Semiconductors
• Silicates
• Minerals

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Perovskite

• Perovskite ABO3 B ? boron
• A2B4O3 A3B3O3 A1B5O3
• CaTiO3 LaAlO3 KNbO3
• Occurs when RA RO and RA gt RB
• CN(B) 6
• CN(A)
• CN(O) 2Ti 4Sr
• CNs make sense?
• Example SrTiO3
• RTi 0.61 Å
• RSr 1.44 Å
• RO 1.36 Å

above/below
12
A
O
B
RTi/RO 0.45 RSr/TO 1.06
http//abulafia.mt.ic.ac.uk/shannon/ptable.php
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Tolerance factor
close-packed directions
A
expect
a
B
t

• Goldschmidt tolerance factor
• 0.88 1.02
• when not 1, structural distortions
• or, perovskite does not form