Q: Which of the following is the correct increasing order of packing efficiency for hcp, bcc and simple cubic lattice?

Explanation:
Packing efficiency refers to the percentage of space in a crystal structure that is occupied by its atoms. It is a measure of how tightly the atoms are packed together in the lattice.

There are three common types of lattice structures to consider:

1. Simple Cubic (SC): In this structure, each unit cell has one atom at each of the eight corners of a cube. However, each corner atom is shared among eight adjacent cubes, so effectively there is only one atom per unit cell. The packing efficiency of the simple cubic lattice is about 52%, which means just over half of the space is occupied by atoms, and the rest is empty space. This makes it the least efficient among the three.

2. Body-Centered Cubic (BCC): The BCC structure also has atoms at each of the eight corners of the cube, but it includes an additional atom at the center of the cube. This results in a total of two atoms per unit cell (each corner atom contributes 1/8th of an atom, and there are eight corners). The packing efficiency of BCC is higher, around 68%, making it more efficient in space utilization compared to simple cubic.

3. Hexagonal Close-Packed (HCP): The HCP structure is arranged so that the atoms are packed closely together in a hexagonal pattern. Each unit cell in HCP contains a larger number of atoms compared to SC and BCC, and its packing efficiency is approximately 74%. This is the highest packing efficiency among the three structures, meaning it uses space most effectively.

Putting it all together, the packing efficiencies increase in the order of simple cubic being the least efficient, followed by body-centered cubic, and hexagonal close-packed being the most efficient.

Therefore, the correct increasing order of packing efficiency is: simple cubic < bcc < hcp