Problem 17 - A Complete Resource Book in Chemistry for JEE Main

Question

The void formed by closed packed array of spheres located at the alternate corners of each face is (a) octahedral void (b) tetrahedral void (c) triangular void (d) both (a) and (b)

Step-by-Step Solution

Answer

The void is an octahedral void (a).

Step 1: Identify Void Types

In crystal structures, spheres can form different types of voids. The common types are octahedral voids and tetrahedral voids. Octahedral voids are formed when there is a space between six spheres, and tetrahedral voids form between four spheres. Triangular void is not typically used in the context of closed-packed structures.

Step 2: Understand Face-Centered Points

The question mentions spheres located at the alternate corners of each face. In a face-centered cubic (FCC) structure, atoms (or spheres) are centered at the corners and the centers of each face of the cube.

Step 3: Locate Spheres at Alternate Corners

If we consider a face of a cube and look at alternate corners, these points would contribute to the corners of an octahedral void. In a face-centered arrangement, each face of the cube contributes to octahedral voids included in the crystal structure.

Step 4: Determine the Void Formed

Since the void is formed by spheres located at the alternate corners of each face, this matches the description of an octahedral void as these positions contribute to forming spaces between six adjacent spheres.

Key Concepts

Octahedral Voids

In a crystal structure, an octahedral void occurs when a group of spheres comes together to create a gap that is surrounded by exactly six spheres. This type of void looks like an octahedron, a shape with eight triangular faces. These voids are crucial in understanding the arrangement of atoms in dense packing.
In a close-packed structure, such as a face-centered cubic (FCC) arrangement, you will often find octahedral voids at strategic points, like at the center of the edges or in the middle of the cube itself.
Octahedral voids play a critical role in allowing certain ions or smaller atoms to fit into the voids. They help in maintaining the stability and predictability of various crystalline materials.

• Octahedral voids require space between six spheres.
• Commonly found in close-packed structures.
• Influences placement and chemical properties of ionic compounds.

Tetrahedral Voids

Tetrahedral voids form when four spheres come together in a cluster within a crystal structure, leaving a smaller gap between them. The formation resembles a tetrahedron, a 3D shape with four triangular faces. These voids are generally smaller than octahedral voids.
In crystal lattices, tetrahedral voids are typically found within the layers of spheres, providing key positions for smaller atoms or ions to reside. These voids significantly influence how structures like metals and ionic crystals pack.
Tetrahedral voids have several important attributes:

• Form a space between four spheres.
• Present in arrangements like face-centered cubic and hexagonal close-packed.
• Impact the physical and chemical properties of materials.

Face-Centered Cubic (FCC) Arrangements

The face-centered cubic (FCC) structure is an efficient way to pack spheres in a crystal lattice. In this configuration, each cube unit consists of atoms at every corner and one in the center of each face, maximizing space utilization.
Because of this tight packing, FCC structures are prevalent in many metals and other crystalline materials. The FCC arrangement ensures that spheres are situated as closely together as possible, resulting in high density and stability.
Some key features of FCC arrangements include:

• Each unit cell has a total of 14 spheres: 8 at the corners and 6 at the face centers.
• Exhibits both octahedral and tetrahedral voids within the structure.
• Common in metals like aluminum, copper, and gold, offering insights into their malleability and ductility.