Why the coordination no. in ABA type arrangement in 3 dimensions is 8....Why not 12?

The coordination number in an ABA type arrangement in three dimensions is indeed 8, and understanding why this is the case involves looking at the geometric arrangement of atoms in a crystal lattice. Let’s break this down step by step.

Understanding Coordination Number

The coordination number refers to the number of nearest neighbor atoms surrounding a central atom in a crystal structure. In the case of an ABA type arrangement, we are typically discussing a structure where 'A' represents one type of atom and 'B' represents another, often seen in ionic compounds or certain alloys.

Examining the ABA Structure

In an ABA arrangement, the 'A' atoms form a face-centered cubic (FCC) lattice, while the 'B' atoms occupy the octahedral sites between them. This arrangement is crucial for determining the coordination number.

Why Coordination Number is 8

In a three-dimensional arrangement, each 'B' atom is surrounded by 'A' atoms. To visualize this, imagine placing a 'B' atom at the center of a cube formed by 'A' atoms at the corners. Each corner of the cube represents a neighboring 'A' atom. Since there are 8 corners in a cube, the coordination number for the 'B' atom is 8.

Why Not 12?

Now, you might wonder why the coordination number isn’t 12. This is because, in the ABA arrangement, the 'B' atoms do not have additional 'A' atoms in the same plane or layer directly above or below them. In a structure with a coordination number of 12, such as in a body-centered cubic (BCC) arrangement, each atom would be surrounded by more neighbors, including those in adjacent layers. However, in the ABA structure, the arrangement is limited to the nearest neighbors, which are the 8 'A' atoms at the corners of the cube.

Visualizing the Concept

To further clarify, think of a cube where each corner is occupied by an 'A' atom. If you were to place a 'B' atom in the center, it would only be directly adjacent to those 8 corner atoms. If you were to try to add more neighbors, you would need to go beyond the nearest neighbors, which is not how coordination numbers are defined.

Examples in Real Life

This concept is commonly observed in ionic compounds like sodium chloride (NaCl), where the sodium ions (Na+) and chloride ions (Cl-) form a similar arrangement. The coordination number reflects the stability and bonding characteristics of the compound, influencing its physical properties.

Summary of Key Points

• The coordination number is the count of nearest neighbors around a central atom.
• In an ABA arrangement, the 'B' atom is surrounded by 8 'A' atoms located at the corners of a cube.
• The limitation to 8 neighbors arises from the specific geometric arrangement of the atoms.

In conclusion, the coordination number of 8 in an ABA type arrangement is a direct result of the spatial configuration of the atoms involved. This arrangement is fundamental in understanding the properties and behaviors of various materials in chemistry and materials science.