Hexagonal

Definition

Hexagonal refers to a crystal structure characterized by a six-fold symmetry, often represented by a two-dimensional lattice that can be described with two basis vectors forming 120-degree angles. This structure is significant in various material properties and is crucial in understanding the arrangements of atoms in solid materials, particularly in the context of Bravais lattices and Miller indices.

5 Must Know Facts For Your Next Test

1. The hexagonal lattice system can be classified into two types: hexagonal close-packed (HCP) and trigonal, where HCP is often found in metals like titanium and magnesium.
2. Hexagonal crystals have three axes of equal length intersecting at 120-degree angles in a plane, with a vertical axis of different length perpendicular to this plane.
3. The symmetry of hexagonal structures plays a significant role in determining physical properties such as anisotropic behavior in elastic and thermal conductivity.
4. In Miller indices, hexagonal systems use a modified notation to represent planes and directions, distinguishing them from cubic or tetragonal systems.
5. Common materials with hexagonal structures include graphite, which has layers of carbon atoms arranged in a hexagonal pattern, leading to its unique electrical and mechanical properties.

Review Questions

• How does the hexagonal lattice system compare to other Bravais lattices in terms of symmetry and atomic arrangement?
  • The hexagonal lattice system differs from other Bravais lattices like cubic or tetragonal by its unique six-fold symmetry and specific geometric arrangement of atoms. While cubic lattices have four symmetrical axes, hexagonal lattices feature three equal-length axes intersecting at 120-degree angles, along with an additional axis perpendicular to this plane. This distinct arrangement influences not only the crystal's shape but also its mechanical and electronic properties.
• Discuss how Miller indices are applied to describe planes in hexagonal crystals and why this is important for understanding their properties.
  • In hexagonal crystals, Miller indices are represented differently than in cubic systems due to their unique geometry. The notation includes four indices (hklm), where 'h' and 'k' correspond to the hexagonal plane's position while 'l' denotes the vertical axis. Understanding how to apply Miller indices allows scientists to communicate about specific planes within hexagonal structures, which is crucial for predicting material behavior under different conditions, such as stress or temperature changes.
• Evaluate the significance of hexagonal crystal structures in materials science, especially regarding their mechanical and thermal properties.
  • Hexagonal crystal structures are significant in materials science due to their influence on mechanical strength and thermal properties. For instance, metals with hexagonal close-packed arrangements tend to exhibit superior ductility and strength compared to those with cubic structures. Moreover, the anisotropic nature of hexagonal materials affects how they conduct heat and electricity, making them valuable for applications requiring specific thermal management or electrical conductivity. Understanding these relationships helps engineers design advanced materials tailored for specific uses.

Related terms

Bravais Lattice: A Bravais lattice is an infinite array of discrete points generated by a set of discrete translation operations, forming the foundational building blocks for describing the periodic arrangement of atoms in crystalline solids.

Unit Cell:

The unit cell is the smallest repeating unit of a crystal lattice that reflects the symmetry and structure of the entire crystal.

Miller Indices:

Miller indices are a notation system in crystallography for planes and directions in crystal lattices, allowing for the classification of crystal structures.