Ionic Model

1
Ionic Model
Lowest energy achieved by maximizing unlike
ion contact (attractions)
minimizing like ion interactions (repulsions)

• A co-ordinated polyhedron of anions will form
  around each cation.
• This will only be stable if the cation is in
  contact with all the anions
• The co-ordination number of the cations will be
  as large as possible

Structures formed in this way will balance the
valance of the cation against the electrostatic
bonds formed with the anions local charge
neutrality.
2
Ionic Model
On the basis of lattice energy we would expect
ionic structures to adopt structures which
maximize their coordination numbers. Large
co-ordination numbers bring anions close
together, so the limit on co-ordination number
for a particular cation will be determined by the
cation/anion size ratio
3
ZnS Blende vs Wurtzite
4R
- 12 1.633R
12 1.915R
4R
- 12 1.633R
1 1.666R
9 1.915R
Blende
Wurtzite
4
ZnS Wurtzite vs Blende
HCP wurtzite1.641
CCP Blende1.638
Many 44 compounds are diamorphic they have
blende and wurtzite forms
Blende Cu (F, Cl, Br, I)Zn (S, Se, Te)Be (S,
Se, Te)Hg (S, Se, Te)Mn (S, Se)
Wurtzite Cd (S, Se)Zn (O, S, Se, Te)BeOHg (S,
Se, Te)Mn (S, Se)
More ionic phases tend to adopted wurtzite form
larger Madelung constant
5
Ionic Model
CsCl 88
CsCl 66
ZnS 44
The observed co-ordination number of cations
should depend only on the ratio of cation and
anion radii
6
Radius Ratio - CsCl
What is the size of the smallest cation which can
reside in a cube of 8 anions ?
Assume the anions are touching, how big is the
interstitial site ?
rC rA (?3 -1)rC/rA 0.732
If the cation is smaller than this it will not be
touching the co-ordinating anions, but they will
be touching each other !
7
Radius Ratio - NaCl
rC rA (?2 -1) rC/rA 0.414
8
Radius Ratio - ZnS
rC rA (1/2?6 -1) rC / rA 0.225
9
Radius Ratios
CsCl 88
CsCl 66
ZnS 44
RC / RA 0.732
RC / RA 0.414
RC / RA 0.225
Ratios represent the minimum cation size for a
given co-ordination number
10
Radius Ratios
rC/rA 0.414
rC/rA 0.732
Li
Na
K
Rb
Cs
I
CsCl
NaCl
Br
Cl
Anion radius (Å)
F
Cation radius (Å)
Radius ratio predict CsCl structure for RbCl and
KCl, but these compounds actually adopt the NaCl
structure.
11
Radius Ratios - Oxides
Radius ratio rules appear to be a good guide for
predicting the local co-ordinationand thus the
structures of binary oxides
Ratios of ionic radii predict octahedral
coordination for all three phases
The high charges on Ti4, Re6 and Mn4 make
these ions highly polarising and thus a truly
ionic interaction is unlikely. It is therefore
more appropriate to use covalent radii.
Ionic radius of O2- 1.26Å, covalent radius of O
0.81 Å. If we use a weighted average 30
ionic, 70 covalent radius of O 0.95 Å
Using weighted radii it is clear that the cations
do not adopt the highest possible co-ordination
number.
Analysing structures using the ionic model is
clearly inappropriate given the degree of
covalency in most solids.