Face-Centered Cubic

Definition

Face-centered cubic (FCC) is a type of crystal structure where atoms are located at each of the corners and the centers of all the faces of the cube. This arrangement results in a high packing efficiency and coordination number, making it an important concept in understanding the geometric properties of polytopes.

5 Must Know Facts For Your Next Test

1. In a face-centered cubic structure, each unit cell contains four atoms, with one atom at each corner and one atom in the center of each face.
2. The face-centered cubic structure has a coordination number of 12, meaning each atom touches 12 other atoms, which contributes to its stability.
3. FCC structures exhibit a packing efficiency of approximately 74%, making them among the most densely packed arrangements of atoms.
4. Common metals that crystallize in the face-centered cubic structure include copper, aluminum, gold, and lead.
5. The geometric arrangement of FCC leads to specific symmetry properties that influence the behavior and characteristics of materials.

Review Questions

• How does the face-centered cubic structure compare to other crystal structures in terms of coordination number and packing efficiency?
  • The face-centered cubic structure has a coordination number of 12 and a packing efficiency of about 74%, which are both higher than many other structures like body-centered cubic (BCC) which has a coordination number of 8 and lower packing efficiency. This efficient packing contributes to the stability and strength of materials with FCC arrangements. Comparing FCC to hexagonal close-packed (HCP) structures shows similar packing efficiencies but different atomic arrangements, which can lead to varying properties in materials.
• Discuss the significance of common metals that exhibit face-centered cubic structures and how this impacts their industrial applications.
  • Metals like copper, aluminum, gold, and lead crystallize in a face-centered cubic structure due to their favorable atomic arrangement that allows for high packing efficiency. This characteristic leads to desirable mechanical properties such as malleability and ductility, making these metals ideal for various industrial applications. For example, copper's excellent conductivity paired with its FCC structure makes it crucial for electrical wiring. Understanding FCC structures helps engineers choose materials suited for specific applications.
• Evaluate how the geometric properties of face-centered cubic structures influence the behavior of materials under stress compared to other arrangements like BCC.
  • The geometric properties of face-centered cubic structures significantly influence how materials behave under stress. The high coordination number and packing efficiency provide FCC metals with greater ductility, allowing them to deform more easily without breaking. In contrast, body-centered cubic structures, while strong, can be more brittle due to lower coordination numbers. Evaluating these differences is crucial in materials science, especially when selecting alloys or designing components that need to withstand varying types of loads or environmental conditions.

Related terms

Coordination Number: The coordination number refers to the number of nearest neighbors surrounding an atom in a crystal structure.

Packing Efficiency: Packing efficiency is the fraction of volume in a crystal structure that is occupied by its constituent particles.

Hexagonal Close-Packed: Hexagonal close-packed (HCP) is another efficient crystal structure where atoms are arranged in a hexagonal lattice, providing a comparison to FCC.