Model Answer
0 min readIntroduction
The stability and structure of minerals are governed by fundamental principles of chemistry and physics, with ionic radius playing a crucial role. The radius ratio, defined as the ratio of the cation radius to the anion radius, is a key parameter influencing the coordination number – the number of anions surrounding a cation in a crystal structure. This ratio dictates the geometrical arrangement of ions, impacting the mineral’s physical and chemical properties. Understanding this relationship is fundamental to interpreting mineral structures and predicting their stability under varying conditions. The concept was pioneered by Linus Pauling, who established rules governing ionic structures based on radius ratio and electrostatic valency.
Radius Ratio and Coordination Number
The radius ratio (r+/r-) is a crucial factor in determining the coordination number of a cation in a mineral structure. Coordination number refers to the number of nearest neighbor anions surrounding a cation. Pauling’s rules state that cations are coordinated by anions in a manner that maximizes electrostatic attraction and minimizes repulsion. Different radius ratio ranges favor different coordination geometries.
Factors Influencing Radius Ratio
- Ionic Charge: Higher charges lead to stronger electrostatic attraction and allow for higher coordination numbers.
- Ionic Size: Larger cations generally prefer higher coordination numbers.
- Polarizability: Anions with higher polarizability can accommodate larger cations, influencing the coordination environment.
Common Coordination Types in Rock-Forming Minerals
1. Six-Fold Coordination (Octahedral Coordination)
A radius ratio between 0.732 and 1.0 is generally favorable for six-fold coordination, where a cation is surrounded by six anions arranged at the corners of an octahedron. This is a very common coordination geometry in rock-forming minerals.
Example: Magnesite (MgCO3). Magnesium (Mg2+) has an ionic radius of 0.72 Å, and oxygen (O2-) has an ionic radius of 1.40 Å. The radius ratio (0.72/1.40 = 0.51) is not directly in the octahedral range, but the presence of the carbonate group (CO32-) and the overall charge balance lead to Mg2+ being octahedrally coordinated by six oxygen atoms. Another example is Peridotite, a common mantle rock, where magnesium is predominantly found in octahedral coordination within olivine and pyroxene minerals.
2. Eight-Fold Coordination (Cubic Coordination)
A radius ratio between 1.0 and 1.55 favors eight-fold coordination, where a cation is surrounded by eight anions arranged at the corners of a cube. This coordination is common in larger cations and is often observed in feldspars and some silicates.
Example: Albite (NaAlSi3O8), a plagioclase feldspar. Sodium (Na+) has an ionic radius of 1.02 Å, and oxygen (O2-) has an ionic radius of 1.40 Å. The radius ratio (1.02/1.40 = 0.73) is close to the lower limit of the cubic coordination range. However, the aluminum ion (Al3+) in the tetrahedral site also influences the overall structure, leading to Na+ being coordinated by eight oxygen atoms. Another example is Sanidine, a high-temperature polymorph of potassium feldspar, where potassium (K+) is typically eight-fold coordinated.
| Coordination Number | Radius Ratio Range (r+/r-) | Geometry | Example Mineral |
|---|---|---|---|
| 6 | 0.732 – 1.0 | Octahedral | Magnesite (MgCO3) |
| 8 | 1.0 – 1.55 | Cubic | Albite (NaAlSi3O8) |
It's important to note that these are idealized ranges, and deviations can occur due to factors like polarization effects and the presence of multiple cations in the structure. Furthermore, the coordination environment can be distorted from perfect geometries due to structural constraints.
Conclusion
In conclusion, the radius ratio is a fundamental parameter governing the coordination number and, consequently, the structure of minerals. The examples of magnesite and albite demonstrate how different radius ratios lead to distinct coordination geometries – octahedral and cubic, respectively – influencing the overall stability and properties of these rock-forming minerals. Understanding this relationship is crucial for interpreting mineral structures, predicting their behavior, and ultimately, deciphering the geological processes that form them. Further research continues to refine our understanding of the complex interplay between ionic radii, charge, and coordination in mineral systems.
Answer Length
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