Key Concepts of Coordination Numbers to Know for Crystallography

Coordination numbers (CN) are crucial in crystallography, representing the number of nearest neighbors around a central atom. They influence the geometry, stability, and properties of crystals, varying based on bonding types and atomic sizes. Understanding CN helps predict crystal behavior.

1. Definition of coordination number

   • Coordination number (CN) refers to the number of nearest neighbor atoms or ions surrounding a central atom in a crystal structure.
   • It is a key factor in determining the geometry and stability of a compound.
   • Coordination numbers can vary based on the type of bonding and the size of the atoms involved.

2. Common coordination numbers (2, 3, 4, 6, 8, 12)

   • CN = 2: Linear coordination, often seen in certain metal complexes.
   • CN = 3: Trigonal planar coordination, common in some small cations.
   • CN = 4: Tetrahedral coordination, typical for many metal ions.
   • CN = 6: Octahedral coordination, prevalent in transition metal complexes.
   • CN = 8: Cubic coordination, found in some ionic compounds.
   • CN = 12: Close-packed coordination, characteristic of metals in a close-packed arrangement.

3. Tetrahedral coordination (CN = 4)

   • Involves four atoms or ions symmetrically arranged around a central atom.
   • Common in compounds like ZnS and SiO2.
   • The bond angles are approximately 109.5°, leading to a three-dimensional structure.

4. Octahedral coordination (CN = 6)

   • Features six atoms or ions surrounding a central atom, forming an octahedron.
   • Common in transition metal complexes, such as [Fe(H2O)6]²⁺.
   • The bond angles are 90°, allowing for efficient packing of ions.

5. Cubic coordination (CN = 8)

   • Involves eight surrounding atoms arranged at the corners of a cube around a central atom.
   • Typically observed in certain ionic compounds like NaCl.
   • Provides a stable structure with a high packing efficiency.

6. Close-packed structures (CN = 12)

   • Characterized by twelve nearest neighbors surrounding a central atom.
   • Common in metals, leading to structures like face-centered cubic (FCC) and hexagonal close-packed (HCP).
   • Maximizes packing efficiency and stability in metallic crystals.

7. Relationship between coordination number and atomic size ratio

   • The coordination number is influenced by the size of the central atom relative to its neighbors.
   • Larger central atoms can accommodate higher coordination numbers due to increased spatial availability.
   • The atomic size ratio helps predict the most stable coordination geometry.

8. Coordination number in ionic compounds

   • Coordination numbers in ionic compounds depend on the charge and size of the ions involved.
   • Higher charges typically lead to higher coordination numbers.
   • Examples include NaCl (CN = 6) and MgO (CN = 6).

9. Coordination number in metallic structures

   • In metals, coordination numbers can vary widely, often ranging from 4 to 12.
   • The coordination number affects the metal's properties, such as conductivity and malleability.
   • Close-packed structures (CN = 12) are common in metals, enhancing stability.

10. Effect of coordination number on crystal properties

    • Coordination number influences the stability, reactivity, and physical properties of crystals.
    • Higher coordination numbers often lead to greater stability and lower energy configurations.
    • The geometry associated with different coordination numbers affects optical and electronic properties of materials.