In which of the following pairs of structures, tetrahedral as well as octahedral holes are found?

Options

A. bcc and fcc
B. hcp and simple cubic
C. hcp and ccp
D. bcc and hcp

Answer

To determine which pairs of structures contain both tetrahedral and octahedral holes, we need to analyze the types of packing in the given structures. Here’s a step-by-step solution:

### Step 1: Understand Tetrahedral and Octahedral Holes
- Tetrahedral holes are formed in a close-packed structure and are located at specific positions relative to the atoms in the lattice.
- Octahedral holes are also found in close-packed structures and are located at different positions compared to tetrahedral holes.

### Step 2: Identify the Structures
The common types of close-packed structures are:
- Hexagonal Close Packing (HCP)
- Face-Centered Cubic (FCC) or Cubic Close Packing (CCP)
- Body-Centered Cubic (BCC)
- Simple Cubic (SC)

### Step 3: Analyze Each Structure
- **HCP and CCP (FCC)**: Both of these structures have a close packing arrangement. They contain both tetrahedral and octahedral voids.
- Tetrahedral voids = 2 per atom (n)
- Octahedral voids = 1 per atom (n)

- **BCC**: This structure does not have a close packing arrangement and contains irregular voids. It has octahedral voids but no tetrahedral voids.

- **Simple Cubic (SC)**: This structure also does not have a close packing arrangement and contains only octahedral voids, but no tetrahedral voids.

### Step 4: Conclusion
From the analysis, we see that:
- HCP and CCP both have tetrahedral and octahedral holes.
- BCC and SC do not have both types of holes.

Thus, the correct answer is the pair that includes HCP and CCP.

### Final Answer
The correct option is **C (HCP and CCP)**.

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