Bravais lattices

Definition

Bravais lattices are distinct arrangements of points in space that represent the periodic structure of a crystal. Each lattice point corresponds to one or more atoms, and these lattices are classified based on their symmetry and geometric properties. They play a critical role in understanding the symmetry in crystals, the characteristics of various crystal systems, and how atoms pack together within those systems.

5 Must Know Facts For Your Next Test

1. There are 14 unique Bravais lattices that can describe all possible three-dimensional periodic structures.
2. Bravais lattices are divided into seven crystal systems based on their symmetry and shape, which include cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic.
3. Each Bravais lattice can be categorized as primitive or non-primitive based on whether lattice points only exist at the corners or include additional points within the unit cell.
4. Common examples of Bravais lattices include the simple cubic lattice found in polonium and the face-centered cubic lattice seen in metals like copper and aluminum.
5. Understanding Bravais lattices helps predict how different materials will behave based on their atomic packing and symmetry properties.

Review Questions

• How do Bravais lattices relate to the concept of symmetry in crystals?
  • Bravais lattices serve as the foundation for understanding crystal symmetry by categorizing the different ways points can be arranged in space. The symmetry elements present in a lattice, such as rotation axes and mirror planes, determine how identical patterns repeat throughout the crystal. This relationship between lattice arrangement and symmetry is essential for identifying physical properties and behaviors of materials.
• Discuss the significance of Bravais lattices in determining atomic packing within crystals.
  • Bravais lattices influence atomic packing by dictating how atoms are arranged within the unit cell. The type of lattice determines whether atoms are close-packed or have interstitial sites available for smaller atoms. Understanding these arrangements allows scientists to predict material properties such as density, stability, and reactivity based on how effectively atoms are packed together.
• Evaluate how different types of Bravais lattices contribute to the characteristics of common crystal structures like NaCl and diamond.
  • Different Bravais lattices define the unique characteristics of common crystal structures by determining how atoms are arranged in three-dimensional space. For instance, NaCl crystallizes in a face-centered cubic Bravais lattice with an alternating arrangement of sodium and chloride ions, leading to its ionic properties. In contrast, diamond adopts a diamond cubic structure derived from a face-centered cubic lattice but with carbon atoms arranged tetrahedrally. These structural differences significantly affect their physical properties, such as hardness and electrical conductivity.

Related terms

Crystal system: A classification of crystals based on their unit cell geometry, which includes parameters like edge lengths and angles between them.

Unit cell: The smallest repeating unit of a crystal lattice that, when stacked in three-dimensional space, recreates the entire crystal structure.

Atomic packing: The arrangement of atoms within a crystal structure, which influences the density and stability of the material.