Bravais lattices

Definition

Bravais lattices are a set of distinct three-dimensional geometric arrangements that describe how points, representing atoms, ions, or molecules, are organized in a crystalline solid. Each lattice type reflects a unique symmetry and periodicity, which helps determine the overall crystal structure and its properties. Understanding Bravais lattices is essential for analyzing how defects can occur in crystals, affecting material behavior and stability.

5 Must Know Facts For Your Next Test

1. There are 14 unique Bravais lattices in three-dimensional space, categorized into seven crystal systems based on their symmetry properties.
2. Bravais lattices can be classified as either primitive or non-primitive, with primitive lattices having lattice points only at the corners and non-primitive having additional points within the unit cell.
3. The choice of a Bravais lattice directly affects the packing efficiency and atomic coordination number, influencing how materials behave under stress or heat.
4. Common examples of Bravais lattices include simple cubic, body-centered cubic, face-centered cubic, hexagonal close-packed, and rhombohedral lattices.
5. Defects such as vacancies or interstitials in a crystal structure can disrupt the Bravais lattice arrangement, leading to changes in mechanical properties like strength and ductility.

Review Questions

• How do the different types of Bravais lattices influence the physical properties of materials?
  • Different types of Bravais lattices impact the physical properties of materials by affecting their atomic packing and coordination numbers. For instance, face-centered cubic structures typically exhibit higher packing efficiency compared to simple cubic structures, resulting in greater density and improved mechanical strength. By understanding how these lattices organize atoms, we can predict how materials will react under various conditions such as stress or temperature changes.
• Compare and contrast primitive and non-primitive Bravais lattices with examples.
  • Primitive Bravais lattices contain lattice points only at the corners of the unit cell, while non-primitive Bravais lattices have additional lattice points within the unit cell. For example, the simple cubic lattice is a primitive lattice with points only at each corner, whereas the body-centered cubic lattice is non-primitive because it has an additional point at the center of the cube. This difference leads to variations in packing efficiency and resulting properties between materials formed from these two types of lattices.
• Evaluate the role of defects in crystals with respect to their Bravais lattice arrangements and overall material performance.
  • Defects in crystals can significantly alter material performance by disrupting the ideal arrangement of atoms defined by their Bravais lattice. For instance, vacancies can lead to reduced strength due to lack of atomic connectivity, while interstitial defects may create stress concentrations that enhance ductility but compromise hardness. Evaluating these interactions allows us to understand how material properties can be tailored for specific applications by manipulating defect concentrations within different Bravais lattice frameworks.

Related terms

Unit cell: The smallest repeating unit of a crystal lattice that can be used to build the entire crystal structure through translation.

Crystal symmetry: The orderly and balanced arrangement of atoms in a crystal structure, which can be described by symmetry operations such as rotations, reflections, and translations.

Defects in crystals: Irregularities or disruptions in the regular arrangement of atoms within a crystal lattice, which can influence the mechanical and thermal properties of materials.