Close packing is maximum in the crystal which is

Options

A. Simple cube
B. bcc
C. fcc
D. None of these

Answer

To determine which crystal structure has maximum close packing, we will analyze the packing efficiency of three types of crystal lattices: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC).

### Step-by-Step Solution:

1. **Understanding Close Packing**:
- Close packing refers to the arrangement of atoms in a crystal structure that maximizes the number of atoms in a given volume. This is quantified by the packing fraction, which is the ratio of the volume occupied by the atoms to the total volume of the unit cell.

2. **Simple Cubic (SC) Structure**:
- In a simple cubic structure, there are 8 atoms located at the corners of the cube.
- Each corner atom contributes \( \frac{1}{8} \) of its volume to the unit cell.
- Therefore, the total number of atoms in a simple cubic unit cell is:
\[ \text{Total atoms} = 8 \times \frac{1}{8} = 1 \text{ atom} \]
- The packing fraction for SC is approximately 52%.

3. **Body-Centered Cubic (BCC) Structure**:
- In a body-centered cubic structure, there are also 8 corner atoms, contributing \( \frac{1}{8} \) each, plus 1 atom at the center of the cube.
- The total number of atoms in a BCC unit cell is:
\[ \text{Total atoms} = 8 \times \frac{1}{8} + 1 = 2 \text{ atoms} \]
- The packing fraction for BCC is approximately 68%.

4. **Face-Centered Cubic (FCC) Structure**:
- In a face-centered cubic structure, there are 8 corner atoms (each contributing \( \frac{1}{8} \)) and 6 face-centered atoms (each contributing \( \frac{1}{2} \)).
- The total number of atoms in an FCC unit cell is:
\[ \text{Total atoms} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \text{ atoms} \]
- The packing fraction for FCC is approximately 74%.

5. **Comparison of Packing Fractions**:
- Simple Cubic: 52%
- Body-Centered Cubic: 68%
- Face-Centered Cubic: 74%

6. **Conclusion**:
- Among the three crystal structures analyzed, the Face-Centered Cubic (FCC) structure has the highest packing fraction (74%), indicating that it has the maximum close packing.

### Final Answer:
The crystal structure with maximum close packing is **Face-Centered Cubic (FCC)**.