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Question

Calculate the packing efficiency in a body centered cubic (BCC) lattice.


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Solution

Step 1: Find the total volume of the unit cell

For Body-Centered Cubic (BCC) lattice, the relationship between the edge length a and the radius r of the unit cell is a=4r3

The volume of the unit cell is

a3=4r33a3=64r333

Step 2: Find the volume occupied by atoms in a unit cell

The volume occupied by one atom is 43πr3

A BCC unit cell has two atoms per unit cell.

The volume occupied by 2 atoms is
2×43πr3=83πr3
Step 3: Find packing efficiency

The packing efficiency=Volume occupied by atoms in a unit celltotal volume of unit cell×100

The packing efficiency of BCC lattice

=83πr364r333×100=68.04%

Thus, the packing efficiency in a body-centered cubic (BCC) lattice is 68.04%


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