upgrade

🌀principles of physics iii review

Hexagonal

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Hexagonal refers to a crystal structure characterized by a geometric arrangement of atoms or molecules in a hexagonal lattice, where each unit cell has six sides. This structure plays a significant role in various materials, including metals, minerals, and some polymers, and influences their properties such as symmetry, density, and strength.

5 Must Know Facts For Your Next Test

  1. The hexagonal structure can be found in various materials like graphite, which has layers of carbon atoms arranged in hexagonal patterns.
  2. In a hexagonal lattice, each atom is surrounded by six other atoms, creating a two-dimensional plane with strong bonding directions.
  3. Hexagonal crystals are often described in terms of two axes: the c-axis, which is perpendicular to the hexagonal base, and the a-axis, which lies within the base.
  4. The coordination number for hexagonal structures is typically 12, indicating that each atom is in contact with 12 neighboring atoms.
  5. Hexagonal close-packed (HCP) and hexagonal diamond are two types of crystal structures that exhibit unique packing efficiencies and properties.

Review Questions

  • How does the hexagonal structure influence the physical properties of materials like graphite?
    • The hexagonal structure of graphite allows for a unique arrangement of carbon atoms that contributes to its exceptional properties. The layers of carbon atoms arranged in a hexagonal lattice are held together by weak van der Waals forces, making them easily slide past one another. This gives graphite its lubricating properties and allows it to conduct electricity due to the mobility of electrons within the hexagonal planes.
  • Compare and contrast hexagonal and cubic crystal structures in terms of their lattice parameters and atomic coordination.
    • Hexagonal and cubic crystal structures differ significantly in their lattice parameters and atomic coordination. In a hexagonal structure, the unit cell is defined by two axes of equal length (a) and one axis (c) that is typically longer. The coordination number is 12. In contrast, cubic structures have all three axes equal in length and exhibit coordination numbers of 8 for simple cubic and 12 for face-centered cubic. These differences affect how atoms pack together and ultimately influence the material properties.
  • Evaluate the significance of hexagonal packing in metals and how it affects their mechanical properties.
    • Hexagonal packing plays a crucial role in determining the mechanical properties of metals that crystallize in this structure, such as titanium and magnesium. The close-packed arrangement allows for efficient use of space and maximizes the density of atoms, which generally enhances strength. Additionally, the orientation of slip systems in hexagonally packed metals affects their ductility and workability under stress. Understanding these relationships helps predict how these metals will behave under different loading conditions.