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Select the correct statements about FCC ...

Select the correct statements about FCC (ABCAB…) Structures.

A

Distance between nearest octahedral void and tetrahedral void is `(sqrt(3)a)/4`

B

Distance between two nearest octahedral void is `a/(sqrt(2))`

C

Distance between two nearest tetrahedral void is `(sqrt(3)a)/2`

D

Distance between layer `A` and `B` is `2rsqrt(2/3)` (`r=` radius of atom)

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the correct statements about FCC (Face-Centered Cubic) structures, we will analyze each statement step by step. ### Step 1: Understanding FCC Structure The FCC structure has atoms located at each corner of the cube and at the centers of each face of the cube. This arrangement leads to the formation of octahedral and tetrahedral voids. ### Step 2: Analyzing the Statements 1. **Statement 1**: The distance between the nearest octahedral void and a tetrahedral void is \( \frac{\sqrt{3}a}{4} \). - In FCC, octahedral voids are located at the edge centers and the body center. The tetrahedral voids are located at positions that are \( \frac{\sqrt{3}}{4} \) of the distance from the body center to the corners. This statement is **correct**. 2. **Statement 2**: The distance between two nearest octahedral voids is \( \frac{a}{\sqrt{2}} \). - The octahedral voids at the edge centers are separated by \( \frac{a}{\sqrt{2}} \) along the edge of the cube. This statement is also **correct**. 3. **Statement 3**: The distance between two tetrahedral voids is \( \frac{\sqrt{3}a}{2} \). - This statement is incorrect. The distance between tetrahedral voids is actually \( \frac{\sqrt{3}a}{4} \), not \( \frac{\sqrt{3}a}{2} \). 4. **Statement 4**: The distance between layer A and B is \( 2R \sqrt{\frac{2}{3}} \) where R is the radius of the atom. - The distance between layers in an FCC structure can be derived from the body diagonal and is indeed \( \frac{2R \sqrt{2}}{3} \). This statement is also **correct**. ### Conclusion The correct statements about FCC structures are: - Statement 1: Correct - Statement 2: Correct - Statement 3: Incorrect - Statement 4: Correct Thus, the correct options are 1, 2, and 4. ### Final Answer The correct statements about FCC (ABCAB…) Structures are statements 1, 2, and 4. ---
To solve the question regarding the correct statements about FCC (Face-Centered Cubic) structures, we will analyze each statement step by step. ### Step 1: Understanding FCC Structure The FCC structure has atoms located at each corner of the cube and at the centers of each face of the cube. This arrangement leads to the formation of octahedral and tetrahedral voids. ### Step 2: Analyzing the Statements 1. **Statement 1**: The distance between the nearest octahedral void and a tetrahedral void is \( \frac{\sqrt{3}a}{4} \). - In FCC, octahedral voids are located at the edge centers and the body center. The tetrahedral voids are located at positions that are \( \frac{\sqrt{3}}{4} \) of the distance from the body center to the corners. This statement is **correct**. ...
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