What is the coordination number of atoms in bcc, hcp and ccp and simple cubic lattices?

Options

A. 8, 12, 12, 6
B. 6, 12, 12, 8
C. 12, 6, 8, 12
D. 12, 12, 8, 6

Answer

To determine the coordination number of atoms in different types of crystal lattices, we need to understand what coordination number means. Coordination number is defined as the number of nearest neighbor atoms or ions that surround a given atom or ion in a crystal structure. Let's analyze the coordination numbers for the body-centered cubic (BCC), hexagonal close-packed (HCP), cubic close-packed (CCP), and simple cubic (SC) lattices step by step.

### Step-by-Step Solution:

1. **Body-Centered Cubic (BCC)**:
- In a BCC lattice, there is one atom located at the center of the cube and eight atoms located at the corners of the cube.
- The atom at the center is surrounded by 8 corner atoms.
- Therefore, the coordination number for BCC is **8**.

2. **Hexagonal Close-Packed (HCP)**:
- In an HCP lattice, each atom is surrounded by 12 other atoms.
- Specifically, there are 6 atoms in the same plane, 3 atoms in the plane above, and 3 atoms in the plane below.
- Thus, the coordination number for HCP is **12**.

3. **Cubic Close-Packed (CCP)**:
- The CCP lattice, also known as face-centered cubic (FCC), has a similar arrangement to HCP in terms of coordination.
- Each atom in the CCP is surrounded by 12 other atoms: 4 in the same plane, 4 in the plane above, and 4 in the plane below.
- Therefore, the coordination number for CCP is also **12**.

4. **Simple Cubic (SC)**:
- In a simple cubic lattice, each atom is at the corners of the cube.
- Each corner atom is in contact with 4 neighboring atoms in the same plane, 1 atom above, and 1 atom below.
- Thus, the coordination number for the simple cubic lattice is **6**.

### Summary of Coordination Numbers:
- BCC: **8**
- HCP: **12**
- CCP: **12**
- Simple Cubic: **6**