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Crystal Chemistry

Pauling's Rules:
  1. Statement of Electroneutrality (part 1): If the total charge on a cation is divided by the number of anions immediately surrounding it (the Coord #), the fraction is the amount of charge the cation contributes to satisfying each anion.

  2. Statement of Electroneutrality (part 2): The fraction of charge received by an anion from neighboring cations, must equal (or approximately equal) it's valency.

  3. Common edges, and especially common faces, between polyhedra diminish stability

    • Shared corners between polyhedra are most common.
        In this configuration the central cations remain ~ far apart.
    • Shared edges are less common.
      • Usually only occur for cubes and octahedrons
      • Very rare for tetrahedrons because central cations of neighboring tetrahedrons come too close together. Repulsion between the positive cation charges creates instabilty.
    • Shared faces are uncommon.
      • will occur for cubes
      • NEVER occurs for tetrahedrons

  4. Corollary to #3: In a crystal containing different cations, those with high valence and low coordination number tend NOT to share polyhedral elements because the repulsive forces are too great.

      i.e., high valence => high charges => strong repulsive forces
        low CN => few surrounding ions => few shielding anions

  5. Principle of Parsimony: The number of essentially different polyhedral constituents in a crystal structure tends to be small (minerals avoid complexity - generally contain 2-3 polyhedra at most).

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