General Bonding considerations

1
General Bonding considerations

• For ionic compounds the bonding forces are
  electrostatic and thus omni-directional. The
  bonding forces should be maximized by packing as
  many cations around each anion and as many
  cations around each anion as is possible. The
  number of nearest neighbor ions of opposite
  charge is called the coordination number. We must
  realize however that the coordination numbers are
  constrained by the stoichiometry of the compound
  by the sizes of the atoms
• e.g. For sodium chloride, NaCl-, there are 6
  anions around each cation (coordination number Na
  6) because of the 11 stoichiometry there must
  also be 6 Na cations around each Cl anion. For
  Zr4O2-2 there are 8 anions around each cation,
  therefore there must be only 4 cations around
  each anion.

2
Ionic Crystal Structures

• Simple ionic crystal structures can be approached
  in terms of the close packing procedures
  developed for metallic structures. It is possible
  to visualize the structures in terms of a close
  packed arrangement of the larger anions, with the
  cations occupying the vacant interstices between
  the close packed layers. Recall that although ccp
  hcp are the most efficient ways of packing
  spheres, only 74 of the available space is
  filled, the 26 "free space" is in the form of
  different types of holes or sites which can be
  occupied by the smaller cations in the ionic
  structures

3
Types of cations sites available in close packed
anion arrays.

• As shown below, the stacking of two close packed
  anion layers produces 2 types of holes.
• One set of holes are octahedrally coordinated by
  6 anions, the second set are tetrahedrally
  coordinated by 4 anions.
• One octahedral site and two tetrahedral sites are
  created by each anion in the close packed layer.

4
Stuffing" of the holes by the cations.

• Having determined what types of holes are
  available we must now decide
• (a) Which sites are occupied by a given cation.
  This determined by the radius ratio (
  rcation/ranion) (b) How many sites are occupied.
  This is determined by the stoichiometry.
• Which sites ? Radius Ratio rules.
• The relative sizes of the anions and cations
  required for a perfect fit of the cation into the
  octahedral sites in a close packed anion array
  can be determined by simple geometry

5
Geometry for cations fitting tetrahedral and
octahedral holes
Similarly for a perfect fit of a cation into the
tetrahedral sites it can be shown that
rcation/ranion 0.225. For these 2 "ideal fit"
radius ratios the anions remain close-packed.
6
Stable Bonding Configurations in Ionic solids.

• In reality an ideal fit of a cation into the
  close packed anion arrangement almost never
  occurs . Now consider what would be the
  consequence of placing a cation that is (a)
  larger than the ideal, (b) smaller than the
  ideal, into the cation sites.
• For a stable coordination the bonded cation and
  anion must be in contact with each other. If the
  cation is larger than the ideal radius ratio
  value the cation and anion remain in contact,
  however the cation forces the anions apart. This
  is not a problem as there is no need for the
  anions to remain in contact.
• If the cation is too small for the site then the
  cation would "rattle" and would not be in contact
  with the surrounding anions. This is an unstable
  bonding configuration.

7
Radius ratio rules for close packed anion
structures

• Circles labeled O represent centers of the
  octahedral interstices in the ccp arrangement of
  anions (fcc unit cell). The cell "owns" 4
  octahedral sites.
• Circles labeled T represent the centers of the
  tetrahedral interstices in the ccp arrangement of
  anions. The cell "owns" 8 tetrahedral sites.

8
Cubic Close Packed (FCC) Anion Arrangement

• Rocksalt (Sodium chloride, NaCl) Structure.
• Anions ccp (fcc). Radius Na 1.02Å, radius Cl-
  1.81Å radius ratio 0.563.
• Therefore Na octahedral.
• 1 octahedral / anion therefore 100 octahedral
  sites are filled.
• Coordination Na 6 coordination Cl 6.
• Na (green) fill the octahedral sites within the
  ccp (ABCABC) anion (red) array
• The face centered cubic unit cell of the NaCl
  structure
• There is an fcc arrangement of the Na cations and
  Cl anions. For an fcc lattice there are 4 lattice
  points per cell. The cell contents are 4 Na
  cations 4 Cl anions.

9
(FCC) Anion Arrangement

• Zincblende (Zinc sulfide, ZnS) structure.
• Anions ccp (fcc). Radius Zn2 0.6Å, radius S2-
  1.84Å radius ratio 0.33
• Have 2 tetrahedral sites/ anion, therefore from
  formula of ZnS only 50 of the tetrahedral sites
  can be filled. Coordination Zn 4
  coordination S 4.
• Which sites are filled ? see picture below.
  Note the filling of diagonally opposite sites to
  maximize the cation-cation separations .

10
CUBIC ANION PACKING

• In these structures the anions are not close
  packed, but occupy just the corners of a cube. In
  this case the center of the cube (surrounded by 8
  anions) can be occupied by a suitably sized
  cation. This site is larger than the tetrahedral
  or octahedral positions in the close packed
  structures. The radius ratio for a perfect fit of
  a cation in a cubic site can again be calculated
  using simple geometry and is 0.73. By including
  the possibility of cubic coordination we can now
  complete our table for predicting cation
  coordinations from the radius ratio rules
  
  
• Cesium Chloride Structure.
• CsCl radius Cs 1.74Å, radius Cl- 1.81Å
  radius ratio 0.96
• All cubic sites are filled by Cs cations.
  Coordination numbers Cs 8 Cl 8. Cs Cl
  are in contact along the body diagonal.

11
FLUORITE STRUCTURE (CaF2).

• Simple cubic arrangement of anions - 50 cubic
  sites filled. e.g.CaF2 ionic radius Ca2
  1.12Å radius F- 1.31Å radius ratio 0.85
• One cubic site per F anion from stoichiometry
  only 50 cubic sites filled by Ca cations.
  Arrangement of the filled cubic sites is such
  that the Ca-Ca distances are as large as possible
  (compare the Ca distribution to that of Zn in
  ZnS) Coordination numbers Ca2 surrounded by 8
  F- 's F- surrounded by 4 Ca2's. Other examples
  ZrO2.