Lesson 2, Topic 4
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Crystal Structure

Abdulaziz July 26, 2020
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When a crystal grows in a constant environment, the form develops as if identical blocks were added continuously.

Crystal Structure = Lattice Point + Basis

Basis = single atom OR group of atoms attached to each lattice point

Lattice points in 3D

  • Lattice points are infinitesimal points in space.
  • Atoms are physical objects.
  • Number, composition and arrangement of atoms is the same for each lattice point.

Unit cell

A lattice point can be described by a vector T with
lattice lengths: the axial length u1, u2, and u3.

Unit Cell = small portion of any given crystal that can be used to reproduce the crystal
Three lattice vectors (a, b, and c, originating from one corner of the unit cell) describe the size and shape of the unit cell vectors.

Parallelepiped unit cell
  • Lattice angles: the inter-axial angles α, β and γ
  • Lattice constants: All of the parameters of the unit cell.
  • Volume:

3D Bravais Lattice Types

Only 14 unique Bravais Lattices (unit cells) to fill space with a periodic arrangement of points.

  • Each lattice point is decorated with the same collection of atoms.
  • Most elemental metals (about 90 %) crystallize into three densely packed crystal structures: bcc, fcc and hcp.

Note: The empty circles refers to the lattice points and not the atoms. You can put any group and size of atoms at these points.