Face-centered cubic

Definition

The face-centered cubic (FCC) structure is a type of crystal lattice arrangement where atoms are located at each of the corners and the centers of all the cube faces. This arrangement allows for a high packing efficiency and contributes to the material's properties, such as ductility and strength. The FCC lattice plays a crucial role in understanding crystal bonding, reciprocal lattices, Miller indices, and crystal growth processes.

5 Must Know Facts For Your Next Test

1. The face-centered cubic lattice has a coordination number of 12, meaning each atom is in contact with 12 other atoms, resulting in strong bonding.
2. Materials with an FCC structure include metals like aluminum, copper, and gold, which exhibit high ductility due to their atomic arrangement.
3. The FCC unit cell contains four atoms per unit cell because each corner atom contributes 1/8th and each face-centered atom contributes 1/2 to the unit cell.
4. The face-centered cubic structure results in a close-packed arrangement, giving it a maximum packing efficiency of about 74%.
5. In reciprocal lattice terms, the FCC lattice corresponds to a body-centered cubic (BCC) structure in reciprocal space, influencing electronic band structure and properties.

Review Questions

• How does the atomic arrangement in a face-centered cubic lattice influence its physical properties?
  • The atomic arrangement in a face-centered cubic lattice greatly affects its physical properties by providing high packing efficiency and a coordination number of 12. This close-packed structure allows for stronger metallic bonding and contributes to the ductility and malleability of materials like aluminum and copper. As atoms can slide past one another more easily, FCC metals typically exhibit better deformation under stress compared to other structures.
• Discuss how Miller indices are used to identify planes in a face-centered cubic crystal structure.
  • Miller indices provide a standardized way to represent the orientation of crystal planes within a face-centered cubic structure. Each plane can be described using three integers that correspond to the intercepts of the plane with the axes of the unit cell. This identification is crucial for analyzing material properties such as diffraction patterns or growth mechanisms, as different planes can exhibit varied atomic arrangements affecting surface energy and reactivity.
• Evaluate the impact of the face-centered cubic structure on the processes involved in crystal growth and wafer preparation.
  • The face-centered cubic structure significantly impacts crystal growth and wafer preparation by influencing nucleation rates and growth patterns. Materials with FCC lattices tend to have smoother surfaces and more uniform growth due to their high symmetry and packing efficiency. Understanding this structure helps in optimizing conditions for crystallization processes, resulting in improved quality of semiconductor wafers essential for electronic applications. Moreover, control over defects in FCC crystals is vital for ensuring the performance of devices made from these materials.

Related terms

Atomic Packing Factor: The fraction of volume in a crystal structure that is occupied by atoms, indicating how tightly atoms are packed together.

Bravais Lattice: A set of 14 distinct lattice types that describe the possible arrangements of points in three-dimensional space, including the FCC structure.

Miller Indices: A notation system in crystallography to denote the orientation of crystal planes, which can be applied to analyze face-centered cubic structures.