Face-centered cubic

Definition

Face-centered cubic (FCC) is a type of crystal lattice structure where atoms are located at each of the corners and the centers of all the faces of the cube. This arrangement allows for a high packing efficiency and coordination number, making it one of the most common structures in metallic solids and other materials. The face-centered cubic structure contributes significantly to the properties and behaviors of materials, such as strength and ductility.

5 Must Know Facts For Your Next Test

1. The face-centered cubic structure has a coordination number of 12, meaning each atom touches 12 other atoms.
2. In an FCC lattice, the atoms are packed with a packing efficiency of approximately 74%, which is one of the highest among all crystal structures.
3. Common metals that exhibit a face-centered cubic structure include aluminum, copper, gold, and silver.
4. The length of the face diagonal in an FCC unit cell is equal to $$ ext{a} \sqrt{2}$$, where 'a' is the edge length of the cube.
5. Face-centered cubic lattices contribute to improved ductility in metals because of their ability to accommodate dislocations more effectively during deformation.

Review Questions

• How does the arrangement of atoms in a face-centered cubic lattice influence its coordination number and packing efficiency?
  • In a face-centered cubic lattice, atoms are located at each corner and at the center of each face of the cube, resulting in a coordination number of 12. This means that each atom is surrounded by 12 nearest neighbors, maximizing the atomic contact within the structure. The packing efficiency of approximately 74% indicates that this arrangement allows for minimal empty space between atoms, making FCC one of the most densely packed crystal structures.
• Discuss how common metals that crystallize in a face-centered cubic structure exhibit unique mechanical properties due to their atomic arrangement.
  • Metals like aluminum, copper, gold, and silver crystallize in a face-centered cubic structure, which provides them with notable mechanical properties such as high ductility and malleability. The high coordination number and packing efficiency enable these metals to accommodate dislocations during deformation. As a result, FCC metals can be easily shaped and manipulated without breaking, making them ideal for various applications in engineering and manufacturing.
• Evaluate the role of face-centered cubic structures in determining the physical properties and behaviors of materials compared to other crystal structures.
  • Face-centered cubic structures play a significant role in determining the physical properties and behaviors of materials due to their high packing efficiency and coordination number. Compared to other structures like body-centered cubic (BCC) or hexagonal close-packed (HCP), FCC metals tend to exhibit greater ductility and lower yield strength. This difference arises from their atomic arrangement that allows for easier slip along certain crystallographic planes during deformation. Understanding these distinctions helps in selecting materials for specific applications based on their mechanical properties.

Related terms

Coordination Number: The number of nearest neighboring atoms surrounding a central atom in a crystal structure.

Packing Efficiency: The fraction of volume in a crystal structure that is occupied by the constituent particles, calculated as the ratio of the volume of the particles to the total volume of the unit cell.

Unit Cell: The smallest repeating unit in a crystal lattice that defines the entire structure's symmetry and properties.