How many number of tetrahedral voids are completely inside the HCP unit cell

Answer

To determine the number of tetrahedral voids that are completely inside the hexagonal close-packed (HCP) unit cell, we can follow these steps:

### Step 1: Understand the Structure of HCP
The HCP structure consists of two layers of atoms arranged in a hexagonal pattern. Each unit cell contains a total of 6 atoms: 2 atoms from the top layer, 2 atoms from the bottom layer, and 2 atoms shared between the two layers.

### Step 2: Identify Tetrahedral Voids
In an HCP unit cell, tetrahedral voids are formed when four atoms are positioned in a tetrahedral arrangement. Each tetrahedral void is surrounded by four atoms.

### Step 3: Calculate Tetrahedral Voids in HCP
In the HCP structure, there are a total of 8 tetrahedral voids per unit cell. This can be understood as follows:
- Each unit cell has 2 tetrahedral voids associated with each of the 6 atoms.
- However, some of these voids are shared between adjacent unit cells.

### Step 4: Count Only the Completely Inside Voids
For the HCP unit cell, only the tetrahedral voids that are completely inside the unit cell are counted. In the case of HCP, there are 8 tetrahedral voids that are completely inside the unit cell.

### Conclusion
Thus, the number of tetrahedral voids that are completely inside the HCP unit cell is **8**.

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