Which of the following is not true about the voids formed in 3 dimensional hexagonal close packed structure?

Options

A. A tetrahedral voids is formed when a sphere of the second layer is present above triangular void in the first layer
B. All the triangular voids are not covered by the spheres of the second layer
C. Tetrahedral voids are formed when the triangular voids in the second layer lie above the triangular voids in the first layer and the triangular shapes of these voids do not overlap
D. Octahedral voids are formed when the triangular voids in the second layer exactly overlap with similar voids in the first layer

Answer

To solve the question regarding the voids formed in a three-dimensional hexagonal close-packed (hcp) structure, we need to analyze the statements provided and determine which one is not true. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Structure of Hexagonal Close Packing
Hexagonal close packing consists of layers of spheres arranged in a specific manner. The arrangement can be visualized in two dimensions first, where each layer is stacked above the previous one, covering some of the voids formed in the layer below.

### Step 2: Analyze Each Statement
We have four statements to evaluate:

1. **Statement 1**: A tetrahedral void is formed when a sphere of the second layer is present above a triangular void in the first layer.
- **Analysis**: This statement is true. In hcp, when a sphere from the second layer is placed above a triangular void formed by three spheres in the first layer, it creates a tetrahedral void.

2. **Statement 2**: All triangular voids are not covered by the spheres of the second layer.
- **Analysis**: This statement is also true. In hcp, only half of the triangular voids are covered by the spheres of the second layer.

3. **Statement 3**: Tetrahedral voids are formed when the triangular voids in the second layer are above the triangular voids in the first layer.
- **Analysis**: This statement is **not true**. When a triangular void in the second layer is above a triangular void in the first layer, it actually forms an octahedral void, not a tetrahedral void.

4. **Statement 4**: Octahedral voids are formed when the triangular voids in the second layer exactly overlap with similar voids in the first layer.
- **Analysis**: This statement is true. When the triangular voids from both layers overlap, they create an octahedral void.

### Step 3: Conclusion
Based on the analysis, the statement that is **not true** is **Statement 3**: "Tetrahedral voids are formed when the triangular voids in the second layer are above the triangular voids in the first layer."

### Final Answer
**Statement 3 is not true.**

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