Face-centered lattice

Definition

A face-centered lattice is a type of three-dimensional arrangement in which atoms are located at each of the corners and the centers of all the cube faces of a unit cell. This structure allows for a high packing efficiency and is significant in understanding crystal systems, particularly in cubic lattices. The arrangement contributes to the unique properties of materials that adopt this structure, making it a key concept when examining lattice types and Bravais lattices.

5 Must Know Facts For Your Next Test

1. In a face-centered lattice, there are four atoms per unit cell: one at each corner (1/8 of an atom per corner) and one at each face center (1/2 of an atom per face).
2. This lattice type has a high atomic packing efficiency of approximately 74%, which is among the highest for any crystal structure.
3. Common metals such as aluminum, copper, and gold crystallize in a face-centered cubic lattice structure.
4. The face-centered lattice exhibits high symmetry, resulting in unique physical properties like increased ductility and malleability in metals.
5. Face-centered lattices belong to the cubic crystal system, which includes other types such as simple cubic and body-centered cubic lattices.

Review Questions

• How does the arrangement of atoms in a face-centered lattice contribute to its packing efficiency compared to other lattice types?
  • The arrangement of atoms in a face-centered lattice allows for a close packing structure, where atoms occupy positions at both the corners and the centers of cube faces. This unique arrangement leads to a packing efficiency of about 74%, which is higher than that of simple cubic lattices. The efficient use of space enhances material properties, making face-centered lattices favorable for metals that require strength and ductility.
• Discuss the significance of coordination number in relation to the face-centered lattice and how it affects material properties.
  • In a face-centered lattice, the coordination number is 12, meaning each atom is surrounded by 12 nearest neighbors. This high coordination number contributes to the stability and strength of materials, impacting their mechanical properties. For instance, metals with this structure often exhibit increased ductility due to their ability to accommodate deformations without fracturing.
• Evaluate how understanding face-centered lattices can aid in predicting the behavior of materials under different conditions.
  • Understanding face-centered lattices is crucial for predicting material behavior because their atomic arrangement influences characteristics like thermal conductivity, electrical conductivity, and malleability. By recognizing that many common metals adopt this structure, scientists can make informed predictions about how these materials will respond to stress, temperature changes, or chemical reactions. This knowledge assists in engineering applications where specific material properties are essential for performance.

Related terms

Cubic lattice: A crystal lattice where the unit cell is in the shape of a cube, characterized by equal edge lengths and right angles between edges.

Coordination number: The number of nearest neighbor atoms surrounding an atom in a crystal lattice, which helps determine the stability and properties of the structure.

Bravais lattice: An infinite array of points generated by repeating a single motif in three-dimensional space, classified into 14 distinct types based on symmetry and arrangement.