Structures of Solids

Introduction to Cubic Unit Cells

• Types of Cubic Unit Cells

  • Simple Cubic

  • Body-Centered Cubic

  • Face-Centered Cubic

• Key Concepts

  • Location of atoms in unit cells

  • Number of atoms per unit cell

  • Coordination numbers

  • Packing efficiencies

Overview of Solid Structures

• Amorphous Solids

  • Example: Glass

  • Lack of regular repeating patterns in crystal structure

Cubic Unit Cells Explained

• Cubic Unit Cell Definition

  • Basic repeating unit is a three-dimensional cube

  • Atoms located at the eight corners of the cube

Simple Cubic

• Atom Locations

  • Atoms only at the eight corners

• Atoms per Unit Cell

  • Each corner contributes 1/8 of an atom

  • Total: 1 atom per unit cell

Body-Centered Cubic

• Atom Locations

  • Atoms at the eight corners and one in the center

• Atoms per Unit Cell

  • Corners contribute 1 atom (8 corners x 1/8)

  • Center contributes 1 atom

  • Total: 2 atoms per unit cell

Face-Centered Cubic

• Atom Locations

  • Atoms at the eight corners and six face centers

• Atoms per Unit Cell

  • Corners contribute 1 atom (8 corners x 1/8)

  • Face centers contribute 3 atoms (6 faces x 1/2)

  • Total: 4 atoms per unit cell

Coordination Numbers

• Definition

  • Number of nearest atom neighbors to a given atom

Simple Cubic

• Coordination Number

  • 6 nearest neighbors (one in each direction)

Body-Centered Cubic

• Coordination Number

  • 8 nearest neighbors (equidistant from body center and corners)

Face-Centered Cubic

• Coordination Number

  • 12 nearest neighbors (4 on the same face and 8 from adjacent layers)

Edge Length and Packing Efficiency

• Edge Length Definition

  • Denoted as "a"

  • For a cube, all edges have the same length

• Relationship to Atomic Radius

  • Edge length "a" equals 2 times the radius for simple cubic

  • For face-centered cubic, atoms touch across a diagonal, not along edges

  • For body-centered cubic, atoms touch along a body diagonal

Calculating Packing Efficiency

• Concept

  • Packing efficiency relates to how closely atoms are packed in a unit cell

• Visualizing Atom Touching

  • Simple cubic: atoms touch along edges

  • Face-centered cubic: atoms touch diagonally across faces

  • Body-centered cubic: atoms touch along body diagonals

Conclusion

• Understanding the structures of solids, particularly cubic unit cells, is essential for grasping the properties of materials in chemistry. This includes knowing the arrangement of atoms, the number of atoms per unit cell, coordination numbers, and how these