Bravais lattices

Definition

Bravais lattices are distinct arrangements of points in space that represent the periodic structure of a crystalline solid. Each lattice point can be thought of as representing an atom, ion, or molecule, and there are 14 unique Bravais lattices in three-dimensional space that describe the symmetry and geometry of crystal structures. Understanding these lattices helps in analyzing how crystals grow and how their physical properties arise from their internal arrangement.

5 Must Know Facts For Your Next Test

1. There are 14 distinct Bravais lattices, which can be categorized into seven crystal systems based on their symmetry properties: cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic.
2. Bravais lattices can be identified by their unique symmetry operations, which include translations, rotations, and reflections that maintain the lattice structure.
3. The concept of Bravais lattices is crucial for determining the physical properties of materials, such as electrical conductivity and optical behavior, based on their crystalline structures.
4. In two-dimensional materials, there are five types of Bravais lattices: square, rectangular, hexagonal, oblique, and centered rectangular.
5. Bravais lattices serve as the foundation for understanding point groups and space groups, which describe the symmetry operations that apply to the entire crystal.

Review Questions

• How do Bravais lattices relate to the growth and physical properties of crystals?
  • Bravais lattices define the periodic arrangement of atoms or molecules within a crystal. This arrangement influences how crystals grow by determining the paths along which atoms add during crystallization. Additionally, the specific type of lattice affects the material's physical properties such as conductivity, strength, and optical characteristics because these properties arise from the atomic arrangement defined by the lattice structure.
• Discuss how symmetry operations are related to Bravais lattices and provide examples.
  • Symmetry operations are actions that can be performed on a crystal lattice that leave its structure unchanged. For Bravais lattices, these operations include translations, rotations, and reflections. For example, in a cubic lattice, rotating around an axis by 90 degrees leaves the structure unchanged due to its symmetry. Understanding these operations is essential when classifying Bravais lattices and determining their corresponding point groups and space groups.
• Evaluate the significance of Bravais lattices in relation to space groups and their implications for crystallography.
  • Bravais lattices are foundational for understanding space groups in crystallography because space groups describe the symmetry of a crystal that combines both translational symmetry from the lattice and additional symmetry from point group operations. Each space group encompasses various symmetries including rotation and reflection that apply to all points within a Bravais lattice. This relationship allows scientists to classify crystals systematically and predict their behavior under various conditions, significantly contributing to fields like solid-state physics and materials science.

Related terms

Unit cell: The smallest repeating unit in a crystal lattice that represents the entire structure when repeated in three-dimensional space.

Lattice parameter: The physical dimensions of the unit cell, including lengths and angles that define the size and shape of the unit cell in a crystal.

Reciprocal lattice: A mathematical construct used in crystallography that represents the Fourier transform of a crystal lattice and is useful for understanding diffraction patterns.