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
Cubic Coordination: CN = 8
2 RA  a
2( RA  rc )  3a
2(rc + RA)
a
 rc  RA  
RA
3
rc
 3  1  0.732
RA
2RA
Cuboctahedral: CN = 12
2RA
rc + RA
rc + RA = 2RA
rc = RA  rc/RA = 1
Radius Ratio Rules
CN (cation)
2
Geometry
linear
min rc/RA (f)
3
trigonal planar
0.155
4
tetrahedral
0.225
6
octahedral
0.414
8
cubic
0.732
12
cubo-octahedral
1
none
if rc is smaller than fRA, then the space is too big and the structure is unstable
Ionic Compounds
anion
cation
Radius Ratio Rules
CN (cation)
2
Geometry
linear
min rc/RA (f)
3
trigonal planar
0.155
4
tetrahedral
sites occur within
0.225
close-packed arrays
6
octahedral
0.414
8
cubic
12
cubo-octahedral
none
common in ionic
compounds
0.732
1
if rc is smaller than fRA, then the space is too big and the structure is unstable
Local Coordination  Structures
• Build up ionic structures from closepacked metallic structures
• Given range of ionic radii: CN = 4, 6, 8
tetrahedral
octahedral
occur in closepacked structures
HCP: tetrahdral sites
4 sites/unit cell
2 sites/close-packed atom
HCP: octahedral sites
2 sites/unit cell
1 site/close-packed atom
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
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
Example: ZnS
• S2- ~ 1.84 Å; Zn2+ ~ 0.60 – 0.57 Å;
– rc/RA = 0.326 – 0.408
•
•
•
•
•
CN
Zn2+ is big enough for CN = 4
4
6
S2- in close-packed array
8
2+
Zn 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
f
0.225
0.414
0.732
ZnS: Zinc Blende
 CCP
anions as CP atoms
fill 4/8 tetr sites
S2y
z=½
z=0
x
x
x
x
x
y
z=½
z=1
x
ZnS: Zinc Blende
S2-
Zn2+
CN(S2-) also = 4
RA/rc > 1  S2- certainly large enough for 4-fold coordination
Example: CaF2 (Fluorite)
•
F-
~ 1.3 Å;
Ca2+
~ 1.0 Å;
– rc/RA = 0.77
• Ca2+ is big enough for CN = 8
CN
f
4
0.225
6
0.414
8
0.732
– 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
Fluorite
Ca2+
FCN(F-) = 4
CN(Ca2+) = 8 [target]