Question

The coordination number for a Body-Centred Cubic (BCC) structure is

• A. 4 atoms
• B. 8 atoms
• C. 9 atoms
• D. 14 atoms

Hint:

In a BCC structure, the coordination number is 8, as the central atom is surrounded by the 8 corner atoms, which are its nearest neighbors.

Answer 1

The Correct Option is B

Step 1: Understand the BCC structure and coordination number.
A Body-Centred Cubic (BCC) structure is a crystal lattice where atoms are positioned at the eight corners of a cube, with an additional atom at the center of the cube. The coordination number is the number of nearest neighboring atoms to a given atom in the lattice. Step 2: Analyze the BCC unit cell.
In a BCC unit cell:
There are 8 atoms at the corners, each shared by 8 unit cells,
contributing \( \frac{1}{8} \times 8 = 1 \) atom per unit cell.
There is 1 atom at the center, fully within the unit cell.
Total atoms per unit cell: \( 1 + 1 = 2 \).
Consider the central atom (body-centered atom) to determine its coordination number:
The central atom is surrounded by the 8 corner atoms.
These 8 corner atoms are the nearest neighbors to the central atom.
Step 3: Calculate the coordination number.
The distance from the central atom to a corner atom can be calculated using the lattice parameter \( a \):
The position of the central atom is at \( (a/2, a/2, a/2) \).
The position of a corner atom (e.g., at the origin) is \( (0, 0, 0) \).
The distance is: \[ \text{Distance} = \sqrt{\left(\frac{a}{2}\right)^2 + \left(\frac{a}{2}\right)^2 + \left(\frac{a}{2}\right)^2} = \sqrt{\frac{3a^2}{4}} = \frac{\sqrt{3}}{2} a. \] This distance is the closest, confirming that the 8 corner atoms are the nearest neighbors.
Thus, the coordination number of the central atom is 8.
For a corner atom, the nearest neighbors are the central atoms of the 8 surrounding unit cells, also giving a coordination number of 8. Hence, the coordination number for BCC is consistently 8.
Step 4: Evaluate the options.
(1) 4 atoms: This is the coordination number for a diamond cubic structure, not BCC. Incorrect.
(2) 8 atoms: Matches the coordination number of BCC. Correct.
(3) 9 atoms: Incorrect for BCC. Incorrect.
(4) 14 atoms: This is the coordination number for some complex structures, but not BCC. Incorrect.
Step 5: Select the correct answer.
The coordination number for a BCC structure is 8, matching option (2).