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HCP (Hexagonal close-packed) is a hexagonal lattice. It is notable (along with FCC) because it achieves the densest possible packing of spheres. It thus arises naturally in many atomic crystals, as well as in colloidal crystals and nanoparticles superlattices.

Canonical HCP

In the canonical HCP, the ratio between the a and c distances is:


  • Crystal Family: Hexagonal
  • Particles per unit cell:
    • 'inner' particles:
    • 'corner' particles:
  • Volume of unit cell:
  • Dimensionality:

Particle Positions (basis vectors)

There are 9 positions, with 2 particles in the unit cell

Particle A: corners

These are the corners of the hexagonal frame. There are 8 corner positions, which contributes a total of 1 particle.

Particle B: inner

Particle Positions (Cartesian coordinates)

Particle A: corners

Particle B: inner

Reciprocal-space Peaks

  • Allowed reflections:
    • even
  • Peak positions:



Many elements pack into HCP. E.g.:

4. Beryllium (Be) (a = b = 2.290 Å, c = 3.588, c/a = 1.567)
27. Cobalt (Co) (a = b = 2.5071 Å, c = 4.0695, c/a = 1.623)
48. Cadmium (Cd) (a =b = 2.9794 Å, c = 5.6186 Å, c/a = 1.886)


  • TBD


See Also