In the close packing arrangement of atoms does a face centred atom touch the face centred atom of an adjacent face? Give reason for your answer

In a close packing arrangement, such as face-centered cubic (FCC) structure, the atoms are arranged in a way that maximizes the efficiency of space utilization. To address your question, let’s delve into the arrangement of atoms in an FCC structure and whether a face-centered atom touches the face-centered atom of an adjacent face.

Understanding Face-Centered Cubic Structure

In an FCC lattice, atoms are located at each of the corners of the cube and at the center of each face. This arrangement allows for a high packing density, which is characteristic of metals like copper, aluminum, and gold.

Atom Arrangement in FCC

To visualize this, imagine a cube where:

• Each corner of the cube has an atom.
• Each face of the cube has an atom at its center.

In total, there are 8 corner atoms and 6 face-centered atoms, but due to the sharing of atoms between adjacent unit cells, the effective number of atoms per unit cell is 4.

Do Face-Centered Atoms Touch Each Other?

Now, let’s focus on your question about whether a face-centered atom touches the face-centered atom of an adjacent face. The answer is no; they do not directly touch each other. Here’s why:

• In an FCC structure, the face-centered atoms are positioned at the center of each face of the cube.
• The distance between the face-centered atoms of adjacent cubes is equal to the face diagonal of the cube.
• The face diagonal can be calculated using the formula: d = a√2, where a is the edge length of the cube.

However, the radius of the atom (r) in an FCC arrangement is related to the edge length by the equation 4r = a√2. This means that the distance between the centers of two adjacent face-centered atoms is greater than the sum of their radii, indicating that they do not touch.

Visualizing the Arrangement

To further clarify, consider this analogy: think of the face-centered atoms as basketballs placed on the center of each face of a cube. If you were to place another basketball on the adjacent face, there would be a gap between them, as they are not directly aligned to touch each other. Instead, the corner atoms of the adjacent cube would be the ones that come into contact with the face-centered atom.

Conclusion

In summary, while face-centered atoms are crucial in the close packing of the FCC structure, they do not touch the face-centered atoms of adjacent faces. Instead, the arrangement allows for efficient packing while maintaining a certain distance between these atoms, which is essential for the stability and properties of the material. Understanding these spatial relationships is key to grasping the fundamentals of crystallography and material science.