Model Answer
0 min readIntroduction
Coordination number, in the context of crystal structures, refers to the number of nearest neighbor ions surrounding a central ion. This number is not arbitrary but is dictated by fundamental chemical principles that govern the stability of ionic bonds. The arrangement of ions in a crystal lattice is a consequence of maximizing attractive forces and minimizing repulsive forces, influenced by factors like ionic radii, charge, and electronegativity. Understanding these parameters is essential for predicting and interpreting the structures of rock-forming minerals, which are the building blocks of Earth’s crust and mantle. This answer will explore these parameters and illustrate them with examples of cations in 3-fold and 4-fold coordination.
Chemical Parameters Determining Coordination Number
Several chemical parameters influence the coordination number of a cation in a crystal structure. The most important are:
- Ionic Radius Ratio (r+/r-): This is the ratio of the cation’s ionic radius to the anion’s ionic radius. Different radius ratios favor different coordination geometries.
- Charge of the Ions (Z+ and Z-): Higher charges lead to stronger electrostatic attraction and can influence the coordination number.
- Electronegativity Difference: A larger electronegativity difference between the cation and anion results in a more ionic bond, impacting the preferred coordination.
- Polarizability of the Anion: Highly polarizable anions can distort their electron clouds to accommodate cations, influencing coordination.
Cations in 3-Fold Coordination (Trigonal Coordination)
3-fold coordination, typically observed in trigonal pyramidal or octahedral-distorted geometries, is favored when the cation is relatively small and has a high charge. This allows it to effectively interact with the surrounding anions without excessive repulsion.
Example: Al3+ in Corundum (α-Al2O3)
Aluminum (Al3+) in corundum is 6-fold coordinated, but the coordination is significantly distorted due to the small size and high charge of Al3+. The Al3+ ion is surrounded by six oxygen ions (O2-) in an octahedrally distorted arrangement. The radius ratio (Al3+/O2- ≈ 0.56) is relatively low, leading to this distortion. The strong electrostatic attraction between Al3+ and O2- necessitates close packing, resulting in a distorted octahedral geometry. The distortion minimizes repulsion between the oxygen ions.
Example: Sc3+ in Beryllia (Be2ScO4)
Scandium (Sc3+) in beryllia exhibits a distorted octahedral coordination. Similar to Al3+, the small ionic radius and high charge of Sc3+ lead to a strong electrostatic interaction with oxygen ions, resulting in a distorted octahedral environment. The radius ratio is also comparable to that of Al3+/O2-.
Cations in 4-Fold Coordination (Tetrahedral Coordination)
4-fold coordination, where a cation is surrounded by four anions in a tetrahedral arrangement, is common for cations with intermediate ionic radii and charges. This geometry allows for a balance between electrostatic attraction and anion-anion repulsion.
Example: Si4+ in Quartz (SiO2)
Silicon (Si4+) in quartz is tetrahedrally coordinated with four oxygen ions (O2-). The radius ratio (Si4+/O2- ≈ 0.40) is ideal for tetrahedral coordination. The tetrahedral arrangement maximizes the distance between the negatively charged oxygen ions, minimizing repulsion. The relatively lower charge of Si4+ compared to Al3+ allows for a more open structure.
Example: Ti4+ in Rutile (TiO2)
Titanium (Ti4+) in rutile is also tetrahedrally coordinated with oxygen ions. The radius ratio (Ti4+/O2- ≈ 0.60) is slightly higher than that of Si4+/O2-, but still favors tetrahedral coordination. The tetrahedral arrangement provides a stable and energetically favorable configuration for Ti4+ and O2- ions.
Relationship between Radius Ratio and Coordination Number
| Coordination Number | Radius Ratio (r+/r-) Range | Geometry |
|---|---|---|
| 3 | 0.155 – 0.225 | Trigonal Planar |
| 4 | 0.225 – 0.414 | Tetrahedral |
| 6 | 0.414 – 0.732 | Octahedral |
| 8 | 0.732 – 1.0 | Cubic |
Conclusion
In conclusion, the coordination number of a cation in a crystal structure is a direct consequence of the interplay between chemical parameters, primarily the ionic radius ratio, charge, and electronegativity. Cations with small radii and high charges, like Al<sup>3+</sup> and Sc<sup>3+</sup>, often exhibit distorted octahedral coordination, while those with intermediate radii and charges, such as Si<sup>4+</sup> and Ti<sup>4+</sup>, commonly adopt tetrahedral coordination. Understanding these relationships is fundamental to predicting and interpreting the structures of rock-forming minerals and, consequently, the properties of the Earth’s materials. Further research into the influence of polarizability and other subtle factors continues to refine our understanding of crystal structure formation.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.