Hexagonal

Definition

Hexagonal refers to a crystal system characterized by a six-fold rotational symmetry, typically forming structures with a distinct six-sided shape. This geometry influences various properties of crystals, including how they pack together and their overall symmetry, connecting closely with aspects such as lattice types and symmetry operations.

5 Must Know Facts For Your Next Test

1. The hexagonal crystal system has four unique lattice parameters: two equal lengths (a) and one distinct length (c), where the angles between them are 90 degrees and 120 degrees.
2. Common minerals that crystallize in the hexagonal system include quartz, beryl, and graphite, showcasing varied physical properties based on their hexagonal arrangement.
3. Hexagonal crystals can exhibit unique optical properties due to their symmetry, such as double refraction seen in minerals like calcite.
4. Symmetry operations in hexagonal crystals often include rotations and reflections that highlight the six-fold axis of symmetry.
5. Hexagonal unit cells are used to define a specific geometric arrangement of atoms in three-dimensional space, which can help in identifying systematic absences during diffraction analysis.

Review Questions

• How does the hexagonal crystal system differ from other crystal systems in terms of symmetry and structure?
  • The hexagonal crystal system is defined by its six-fold rotational symmetry and distinctive unit cell geometry, which includes two equal lengths and one different length. This sets it apart from other systems like cubic or tetragonal, which have different symmetries and arrangements. The hexagonal structure allows for specific packing configurations and affects the physical properties of materials formed within this system.
• Discuss how hexagonal symmetry impacts the classification of point groups in crystallography.
  • Hexagonal symmetry plays a significant role in defining point groups, particularly those that exhibit six-fold rotational axes. This leads to a classification of crystals that can be grouped based on their symmetrical features. For example, crystals with hexagonal symmetry can belong to various point groups that include operations such as rotation, reflection, and inversion, significantly influencing their crystallographic behavior and interactions with external forces.
• Evaluate the importance of hexagonal unit cells in the determination of crystal structures using diffraction methods.
  • Hexagonal unit cells are crucial for accurately determining crystal structures through techniques such as X-ray diffraction. The unique geometry and arrangement of atoms within these cells lead to specific patterns in diffraction data. By analyzing systematic absences associated with hexagonal lattices, researchers can deduce important structural information about the material being studied, enhancing our understanding of its properties and potential applications.

Related terms

Trigonal: A crystal system with three-fold rotational symmetry that can sometimes overlap with hexagonal in certain lattice arrangements.

Bravais Lattice: One of the distinct lattice types that describes the arrangement of points in space, including hexagonal lattices which have specific symmetry and packing characteristics.

Point Group: A set of symmetry operations that leave at least one point unchanged, which can include groups associated with hexagonal symmetry.