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In which of the following arrangement...

In which of the following arrangements, Octahedral voids are formed ?

A

hcp

B

bcc

C

simple cubic

D

fcc.

Text Solution

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The correct Answer is:
To determine in which arrangements octahedral voids are formed, we need to analyze the structures mentioned in the options: Simple Cubic (SCP), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). ### Step-by-Step Solution: 1. **Understanding Octahedral Voids**: - Octahedral voids are formed when atoms are arranged in such a way that there are empty spaces that can accommodate another atom. These voids are typically located at specific positions in the unit cell. 2. **Analyzing Simple Cubic (SCP)**: - In a Simple Cubic structure, atoms are located at the corners of the cube. - The only octahedral void present is at the body center of the cube. - Therefore, octahedral voids are formed in the Simple Cubic structure. 3. **Analyzing Body-Centered Cubic (BCC)**: - In a Body-Centered Cubic structure, there are atoms at each corner and one atom at the center of the cube. - The body center is occupied by an atom, and there are no additional octahedral voids present. - Thus, octahedral voids are **not** formed in the BCC structure. 4. **Analyzing Face-Centered Cubic (FCC)**: - In a Face-Centered Cubic structure, atoms are located at each corner and at the centers of each face of the cube. - Octahedral voids are present at the body center and at the edge centers of the cube. - Therefore, octahedral voids are formed in the FCC structure. 5. **Conclusion**: - Based on the analysis: - Octahedral voids are formed in **Simple Cubic (SCP)** and **Face-Centered Cubic (FCC)** arrangements. - They are **not** formed in **Body-Centered Cubic (BCC)**. ### Final Answer: The arrangements in which octahedral voids are formed are: - **Option A: Simple Cubic (SCP)** - **Option D: Face-Centered Cubic (FCC)**
To determine in which arrangements octahedral voids are formed, we need to analyze the structures mentioned in the options: Simple Cubic (SCP), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). ### Step-by-Step Solution: 1. **Understanding Octahedral Voids**: - Octahedral voids are formed when atoms are arranged in such a way that there are empty spaces that can accommodate another atom. These voids are typically located at specific positions in the unit cell. 2. **Analyzing Simple Cubic (SCP)**: ...
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In HCP or CCP constituent particles occupy 74% of the available space. The remaining space (26%) in between the spheres remains unoccupied and is called interstitial voids or holes. Considering the close packing arrangement, each sphere in the second layer rests on the hollow space of the first layer, touching each other. The void created is called tetrahedral void. If R is the radius of the spheres in the close packed arrangement then, R (radius of tetrahedral void) = 0.225 R In a close packing arrangement, the interstitial void formed by the combination of two triangular voids of the first and second layer is called octahedral coid. Thus, double triangular void is surrounded by six spheres. The centre of these spheres on joining, forms octahedron. If R is the radius of the sphere. in a close packed arrangement then, R (radius of octahedral void = 0.414 R). In Schottky defect

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