The correct statement/statements is/are:

Options

A. The distance between two octahedral voids of a cubic close packing of atoms with radius `r` is `2r`
B. The distance between two tetrahedral voids of a cubic close packing of atoms with radius `r` is `sqrt(6)xxr` at the body diagonal axes
C. The distance between tetrahedral and octehedral void is `sqrt(3/2)xxr`, where is the radius of atom forming the close packing
D. The distance between the surface of atoms `fcc` arrangement along an edge is `2(sqrt(2)-1)r`

Explanation

To determine the correct statements regarding the distances between voids in cubic close packing (CCP) of atoms, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Octahedral Voids:**
- In cubic close packing, octahedral voids are located at the center of the unit cell and at the edge centers.
- The distance between two octahedral voids (one at the center and one at the edge) is calculated as:
\[ \text{Distance} = 2r \]
- **Conclusion:** The first statement is correct.

2. **Understanding Tetrahedral Voids:**
- Tetrahedral voids in cubic close packing are located at specific positions, including along the body diagonal.
- The distance between the two tetrahedral voids along the body diagonal is given by:
\[ \text{Distance} = \sqrt{6}r \]
- **Conclusion:** The second statement is correct.

3. **Distance Between Tetrahedral and Octahedral Voids:**
- The distance between a tetrahedral void and an octahedral void can be derived from their positions in the unit cell.
- The distance is calculated as:
\[ \text{Distance} = \frac{\sqrt{3}}{2}r \]
- **Conclusion:** The third statement is correct.

4. **Distance Between Surface Atoms Along an Edge:**
- The distance between the surface of atoms arranged along an edge in a cubic close packing structure is given by:
\[ \text{Distance} = 2\sqrt{2}r \]
- However, the statement mentions \(2\sqrt{-1}r\), which is incorrect as it does not represent a valid distance.
- **Conclusion:** The fourth statement is incorrect.

### Final Conclusion:
- The correct statements are the first three:
1. The distance between two octahedral voids is \(2r\).
2. The distance between two tetrahedral voids is \(\sqrt{6}r\).
3. The distance between tetrahedral and octahedral voids is \(\frac{\sqrt{3}}{2}r\).
- The fourth statement is incorrect.