Themes of the Day:

• Structure Controls in Ionic Bonding (Pauling's Rules)

Structure Controls in Ionic Bonding

• Rule 1: The Coordination Principle
  • Coordination Number (CN) is a function of the Radius Ratio (RR); RR = R_c/R_a

  • Coordination Number (CN)	Polyhedron	Radius Ratio (RR)
    12	Not Regular; based on cubic or hexagonal closest packing	~1
    8	Cube	0.732 - 1
    6	Octahedron	0.414 - 0.732
    4	Tetrahedron	0.225 - 0.414
    3	Triangle	0.155 - 0.225
    2	Line	< 0.155

  • Figure 4.3
• Rule 2: The Electrostatic Valency Principle
  • evb = ion charge/CN
  • Uniform Bond Strength: Isodesmic - e.g., halite
  • Non-Uniform Bond Strength: Anisodesmic - e.g., carbonate group; anhydrite
  • Non-Uniform Bond Strength: Mesodesmic - e.g., silica tetrahedra
• Rule 3: Sharing of Polyhedral Elements I - sharing corners preferable to edges preferable to faces
• Rule 4: Sharing of Polyhedral Elements II - small, high charge cation polyhedra prefer not to be in adjacent polyhedra
• Rule 5: Principle of Parsimony - fundamentally few different structural sites in any mineral