Identify each of the following kinds of packing: (d)

Verified step by step guidance

1. Observe the image provided, which shows a unit cell with a red sphere at the center and blue spheres at the corners.
2. Identify the type of unit cell based on the arrangement of spheres. The red sphere at the center and blue spheres at the corners indicate a specific type of packing.
3. Recognize that this arrangement is characteristic of a body-centered cubic (BCC) unit cell.
4. In a BCC unit cell, there is one atom at each corner of the cube and one atom in the center of the cube.
5. Conclude that the given image represents a body-centered cubic (BCC) packing.

Key Concepts

Body-Centered Cubic (BCC) Structure

The body-centered cubic (BCC) structure is a type of crystal lattice where one atom is located at each of the eight corners of a cube and a single atom is positioned at the center of the cube. This arrangement results in a coordination number of 8, meaning each central atom is surrounded by eight corner atoms. BCC structures are commonly found in metals like iron and chromium, influencing their physical properties.

Coordination Number

The coordination number refers to the number of nearest neighbor atoms surrounding a central atom in a crystal structure. In the case of the BCC structure, the coordination number is 8, indicating that each atom at the center is in contact with eight corner atoms. This concept is crucial for understanding the packing efficiency and stability of different crystal structures.

Packing Efficiency

Packing efficiency is a measure of how effectively atoms are packed in a crystal structure, expressed as the ratio of the volume occupied by the atoms to the total volume of the unit cell. In BCC structures, the packing efficiency is approximately 68%, which is lower than that of face-centered cubic (FCC) structures. Understanding packing efficiency helps in predicting the properties of materials, such as density and strength.